diff --git a/muted-tests.yml b/muted-tests.yml
index 317f0dbe6abc4..65d3417a2a6d3 100644
--- a/muted-tests.yml
+++ b/muted-tests.yml
@@ -426,9 +426,6 @@ tests:
 - class: org.elasticsearch.backwards.MixedClusterClientYamlTestSuiteIT
   method: test {p0=search/350_point_in_time/point-in-time with index filter}
   issue: https://github.com/elastic/elasticsearch/issues/127741
-- class: org.elasticsearch.compute.aggregation.FilteredGroupingAggregatorFunctionTests
-  method: testSimpleCircuitBreaking
-  issue: https://github.com/elastic/elasticsearch/issues/127833
 - class: org.elasticsearch.packaging.test.DockerTests
   method: test025SyncPluginsUsingProxy
   issue: https://github.com/elastic/elasticsearch/issues/127138
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/AggregatorFunctionTestCase.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/AggregatorFunctionTestCase.java
index 3f47be19b22e1..ceb6978dc81e8 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/AggregatorFunctionTestCase.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/AggregatorFunctionTestCase.java
@@ -61,7 +61,7 @@ protected final int aggregatorIntermediateBlockCount() {
     protected abstract void assertSimpleOutput(List<Block> input, Block result);
 
     @Override
-    protected Operator.OperatorFactory simpleWithMode(AggregatorMode mode) {
+    protected Operator.OperatorFactory simpleWithMode(SimpleOptions options, AggregatorMode mode) {
         return simpleWithMode(mode, Function.identity());
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/GroupingAggregatorFunctionTestCase.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/GroupingAggregatorFunctionTestCase.java
index 9b8246be49799..d90a3ac827872 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/GroupingAggregatorFunctionTestCase.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/aggregation/GroupingAggregatorFunctionTestCase.java
@@ -90,8 +90,8 @@ protected DataType acceptedDataType() {
     };
 
     @Override
-    protected final Operator.OperatorFactory simpleWithMode(AggregatorMode mode) {
-        return simpleWithMode(mode, Function.identity());
+    protected final Operator.OperatorFactory simpleWithMode(SimpleOptions options, AggregatorMode mode) {
+        return simpleWithMode(options, mode, Function.identity());
     }
 
     protected List<Integer> channels(AggregatorMode mode) {
@@ -99,6 +99,7 @@ protected List<Integer> channels(AggregatorMode mode) {
     }
 
     private Operator.OperatorFactory simpleWithMode(
+        SimpleOptions options,
         AggregatorMode mode,
         Function<AggregatorFunctionSupplier, AggregatorFunctionSupplier> wrap
     ) {
@@ -108,13 +109,24 @@ private Operator.OperatorFactory simpleWithMode(
         if (randomBoolean()) {
             supplier = chunkGroups(emitChunkSize, supplier);
         }
-        return new RandomizingHashAggregationOperatorFactory(
-            List.of(new BlockHash.GroupSpec(0, ElementType.LONG)),
-            mode,
-            List.of(supplier.groupingAggregatorFactory(mode, channels(mode))),
-            randomPageSize(),
-            null
-        );
+
+        if (options.requiresDeterministicFactory()) {
+            return new HashAggregationOperator.HashAggregationOperatorFactory(
+                List.of(new BlockHash.GroupSpec(0, ElementType.LONG)),
+                mode,
+                List.of(supplier.groupingAggregatorFactory(mode, channels(mode))),
+                randomPageSize(),
+                null
+            );
+        } else {
+            return new RandomizingHashAggregationOperatorFactory(
+                List.of(new BlockHash.GroupSpec(0, ElementType.LONG)),
+                mode,
+                List.of(supplier.groupingAggregatorFactory(mode, channels(mode))),
+                randomPageSize(),
+                null
+            );
+        }
     }
 
     @Override
@@ -389,6 +401,7 @@ public final void testEmptyInput() {
 
     public final void testAllFiltered() {
         Operator.OperatorFactory factory = simpleWithMode(
+            SimpleOptions.DEFAULT,
             AggregatorMode.SINGLE,
             agg -> new FilteredAggregatorFunctionSupplier(agg, ConstantBooleanExpressionEvaluator.factory(false))
         );
@@ -401,6 +414,7 @@ public final void testAllFiltered() {
 
     public final void testNoneFiltered() {
         Operator.OperatorFactory factory = simpleWithMode(
+            SimpleOptions.DEFAULT,
             AggregatorMode.SINGLE,
             agg -> new FilteredAggregatorFunctionSupplier(agg, ConstantBooleanExpressionEvaluator.factory(true))
         );
@@ -414,6 +428,7 @@ public final void testNoneFiltered() {
 
     public void testSomeFiltered() {
         Operator.OperatorFactory factory = simpleWithMode(
+            SimpleOptions.DEFAULT,
             AggregatorMode.SINGLE,
             agg -> new FilteredAggregatorFunctionSupplier(agg, AddGarbageRowsSourceOperator.filterFactory())
         );
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneCountOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneCountOperatorTests.java
index 4c97c78fdda95..bf0575821fbe6 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneCountOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneCountOperatorTests.java
@@ -51,7 +51,7 @@ public void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneCountOperator.Factory simple() {
+    protected LuceneCountOperator.Factory simple(SimpleOptions options) {
         return simple(randomFrom(DataPartitioning.values()), between(1, 10_000), 100);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMaxOperatorTestCase.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMaxOperatorTestCase.java
index 5b3b0b6c63b2d..6275b3a07cacb 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMaxOperatorTestCase.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMaxOperatorTestCase.java
@@ -73,7 +73,7 @@ public void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneMaxFactory simple() {
+    protected LuceneMaxFactory simple(SimpleOptions options) {
         return simple(getNumberTypeTest(), randomFrom(DataPartitioning.values()), between(1, 10_000), 100);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMinOperatorTestCase.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMinOperatorTestCase.java
index 298701c4f7cd7..cf1620b309010 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMinOperatorTestCase.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneMinOperatorTestCase.java
@@ -73,7 +73,7 @@ public void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneMinFactory simple() {
+    protected LuceneMinFactory simple(SimpleOptions options) {
         return simple(getNumberTypeTest(), randomFrom(DataPartitioning.values()), between(1, 10_000), 100);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneSourceOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneSourceOperatorTests.java
index 6aacf4a6c3bf1..a7de1ddf74ec2 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneSourceOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneSourceOperatorTests.java
@@ -72,7 +72,7 @@ public void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneSourceOperator.Factory simple() {
+    protected LuceneSourceOperator.Factory simple(SimpleOptions options) {
         return simple(randomFrom(DataPartitioning.values()), between(1, 10_000), 100, scoring);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorScoringTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorScoringTests.java
index 786cbd76f2efd..9a558f69eb6ef 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorScoringTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorScoringTests.java
@@ -58,7 +58,7 @@ private void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneTopNSourceOperator.Factory simple() {
+    protected LuceneTopNSourceOperator.Factory simple(SimpleOptions options) {
         return simple(DataPartitioning.SHARD, 10_000, 100);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorTests.java
index 7a1ee32e7a42d..a43c37979a94e 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/LuceneTopNSourceOperatorTests.java
@@ -63,7 +63,7 @@ private void closeIndex() throws IOException {
     }
 
     @Override
-    protected LuceneTopNSourceOperator.Factory simple() {
+    protected LuceneTopNSourceOperator.Factory simple(SimpleOptions options) {
         return simple(DataPartitioning.SHARD, 10_000, 100);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/TimeSeriesSourceOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/TimeSeriesSourceOperatorTests.java
index 4ab74eabd7463..4cb6dac14c151 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/TimeSeriesSourceOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/TimeSeriesSourceOperatorTests.java
@@ -328,7 +328,7 @@ public void testMatchNone() throws Exception {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return createTimeSeriesSourceOperator(directory, r -> this.reader = r, randomBoolean(), List.of(), 1, 1, false, writer -> {
             long timestamp = DateFieldMapper.DEFAULT_DATE_TIME_FORMATTER.parseMillis("2024-01-01T00:00:00Z");
             writeTS(writer, timestamp, new Object[] { "hostname", "host-01" }, new Object[] { "voltage", 2 });
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValueSourceReaderTypeConversionTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValueSourceReaderTypeConversionTests.java
index 3778b6965b4f3..55c7b95d1edf0 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValueSourceReaderTypeConversionTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValueSourceReaderTypeConversionTests.java
@@ -216,7 +216,7 @@ private IndexReader reader(String indexKey) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return factory(initShardContexts(), mapperService("index1").fieldType("long"), ElementType.LONG);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValuesSourceReaderOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValuesSourceReaderOperatorTests.java
index 60d160b67154a..a0fae75fd6200 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValuesSourceReaderOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/lucene/ValuesSourceReaderOperatorTests.java
@@ -127,7 +127,7 @@ public void closeIndex() throws IOException {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         if (reader == null) {
             // Init a reader if one hasn't been built, so things don't blow up
             try {
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/AggregationOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/AggregationOperatorTests.java
index 6fbef583cbefa..2408e758ec697 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/AggregationOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/AggregationOperatorTests.java
@@ -35,7 +35,7 @@ protected SourceOperator simpleInput(BlockFactory blockFactory, int size) {
     }
 
     @Override
-    protected Operator.OperatorFactory simpleWithMode(AggregatorMode mode) {
+    protected Operator.OperatorFactory simpleWithMode(SimpleOptions options, AggregatorMode mode) {
         List<Integer> sumChannels, maxChannels;
         if (mode.isInputPartial()) {
             int sumInterChannelCount = SumLongAggregatorFunction.intermediateStateDesc().size();
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ChangePointOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ChangePointOperatorTests.java
index 3175bb06c5627..d3e68fc603cf9 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ChangePointOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ChangePointOperatorTests.java
@@ -70,7 +70,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new ChangePointOperator.Factory(0, null, 0, 0);
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnExtractOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnExtractOperatorTests.java
index bd38967be7e34..f3bc02ffe5845 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnExtractOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnExtractOperatorTests.java
@@ -48,7 +48,7 @@ public String toString() {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         Supplier<ColumnExtractOperator.Evaluator> expEval = () -> new FirstWord(0);
         return new ColumnExtractOperator.Factory(
             new ElementType[] { ElementType.BYTES_REF },
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnLoadOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnLoadOperatorTests.java
index 3bcecda2ff9e5..2104fdcc42c6e 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnLoadOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ColumnLoadOperatorTests.java
@@ -64,7 +64,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new ColumnLoadOperator.Factory(
             new ColumnLoadOperator.Values(
                 "values",
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/EvalOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/EvalOperatorTests.java
index 85f4804653157..544541ef49d29 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/EvalOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/EvalOperatorTests.java
@@ -68,7 +68,7 @@ public void close() {}
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new EvalOperator.EvalOperatorFactory(new EvalOperator.ExpressionEvaluator.Factory() {
             @Override
             public EvalOperator.ExpressionEvaluator get(DriverContext context) {
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/FilterOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/FilterOperatorTests.java
index ce85d9baa5c7d..a0de030bf4c97 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/FilterOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/FilterOperatorTests.java
@@ -54,7 +54,7 @@ public void close() {}
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new FilterOperator.FilterOperatorFactory(new EvalOperator.ExpressionEvaluator.Factory() {
 
             @Override
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ForkingOperatorTestCase.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ForkingOperatorTestCase.java
index 7d1471a0f3ebf..b48135c3f2bdd 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ForkingOperatorTestCase.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ForkingOperatorTestCase.java
@@ -54,11 +54,18 @@ public abstract class ForkingOperatorTestCase extends OperatorTestCase {
 
     private static final String ESQL_TEST_EXECUTOR = "esql_test_executor";
 
-    protected abstract Operator.OperatorFactory simpleWithMode(AggregatorMode mode);
+    protected abstract Operator.OperatorFactory simpleWithMode(SimpleOptions options, AggregatorMode mode);
+
+    /**
+     * Calls {@link #simpleWithMode(SimpleOptions, AggregatorMode)} with the default options.
+     */
+    protected final Operator.OperatorFactory simpleWithMode(AggregatorMode mode) {
+        return simpleWithMode(SimpleOptions.DEFAULT, mode);
+    }
 
     @Override
-    protected final Operator.OperatorFactory simple() {
-        return simpleWithMode(AggregatorMode.SINGLE);
+    protected final Operator.OperatorFactory simple(SimpleOptions options) {
+        return simpleWithMode(options, AggregatorMode.SINGLE);
     }
 
     public final void testInitialFinal() {
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/HashAggregationOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/HashAggregationOperatorTests.java
index 30579f864abcb..0bacb36e00066 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/HashAggregationOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/HashAggregationOperatorTests.java
@@ -41,7 +41,7 @@ protected SourceOperator simpleInput(BlockFactory blockFactory, int size) {
     }
 
     @Override
-    protected Operator.OperatorFactory simpleWithMode(AggregatorMode mode) {
+    protected Operator.OperatorFactory simpleWithMode(SimpleOptions options, AggregatorMode mode) {
         List<Integer> sumChannels, maxChannels;
         if (mode.isInputPartial()) {
             int sumChannelCount = SumLongAggregatorFunction.intermediateStateDesc().size();
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorAppendPageTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorAppendPageTests.java
index e9d9ce7c70fdf..a355e3021d8bf 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorAppendPageTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorAppendPageTests.java
@@ -103,7 +103,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new IteratorAppendPage.Factory();
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorRemovePageTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorRemovePageTests.java
index c682a2960b380..77b2120002d92 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorRemovePageTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/IteratorRemovePageTests.java
@@ -105,7 +105,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new IteratorRemovePage.Factory();
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/LimitOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/LimitOperatorTests.java
index bf0e01bc59618..8740ec8135783 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/LimitOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/LimitOperatorTests.java
@@ -27,7 +27,7 @@
 
 public class LimitOperatorTests extends OperatorTestCase {
     @Override
-    protected LimitOperator.Factory simple() {
+    protected LimitOperator.Factory simple(SimpleOptions options) {
         return new LimitOperator.Factory(100);
     }
 
@@ -55,7 +55,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
 
     public void testStatus() {
         BlockFactory blockFactory = driverContext().blockFactory();
-        LimitOperator op = simple().get(driverContext());
+        LimitOperator op = simple(SimpleOptions.DEFAULT).get(driverContext());
 
         LimitOperator.Status status = op.status();
         assertThat(status.limit(), equalTo(100));
@@ -77,7 +77,7 @@ public void testStatus() {
 
     public void testNeedInput() {
         BlockFactory blockFactory = driverContext().blockFactory();
-        try (LimitOperator op = simple().get(driverContext())) {
+        try (LimitOperator op = simple(SimpleOptions.DEFAULT).get(driverContext())) {
             assertTrue(op.needsInput());
             Page p = new Page(blockFactory.newConstantNullBlock(10));
             op.addInput(p);
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/MvExpandOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/MvExpandOperatorTests.java
index d6abdac383e5c..cd88356a0d3eb 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/MvExpandOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/MvExpandOperatorTests.java
@@ -49,7 +49,7 @@ protected Page createPage(int positionOffset, int length) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new MvExpandOperator.Factory(0, randomIntBetween(1, 1000));
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/OutputOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/OutputOperatorTests.java
index 8a6e890afde2b..8947f7ca5aded 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/OutputOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/OutputOperatorTests.java
@@ -17,7 +17,7 @@
 
 public class OutputOperatorTests extends AnyOperatorTestCase {
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new OutputOperator.OutputOperatorFactory(List.of("a"), p -> p, p -> {});
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ProjectOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ProjectOperatorTests.java
index 12b22a6244ae3..de32b51f93edb 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ProjectOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/ProjectOperatorTests.java
@@ -66,7 +66,7 @@ protected SourceOperator simpleInput(BlockFactory blockFactory, int end) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new ProjectOperator.ProjectOperatorFactory(Arrays.asList(1));
     }
 
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/RowInTableLookupOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/RowInTableLookupOperatorTests.java
index 7522f57a3a9ee..63f8239073c2a 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/RowInTableLookupOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/RowInTableLookupOperatorTests.java
@@ -79,7 +79,7 @@ private void assertSimpleOutput(List<Page> input, List<Page> results, int keyCha
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         return new RowInTableLookupOperator.Factory(
             new RowInTableLookupOperator.Key[] {
                 new RowInTableLookupOperator.Key(
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/SampleOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/SampleOperatorTests.java
index cf2d73ab4768f..c66c48d2af783 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/SampleOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/SampleOperatorTests.java
@@ -40,7 +40,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected SampleOperator.Factory simple() {
+    protected SampleOperator.Factory simple(SimpleOptions options) {
         return new SampleOperator.Factory(0.5, randomInt());
     }
 
@@ -59,7 +59,7 @@ public void testAccuracy() {
         int totalPositionCount = 0;
 
         for (int iter = 0; iter < 10000; iter++) {
-            SampleOperator operator = simple().get(driverContext());
+            SampleOperator operator = simple(SimpleOptions.DEFAULT).get(driverContext());
             operator.addInput(new Page(blockFactory.newConstantNullBlock(20000)));
             Page output = operator.getOutput();
             // 10000 expected rows, stddev=sqrt(10000)=100, so this is 10 stddevs.
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/StringExtractOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/StringExtractOperatorTests.java
index 09105774388a2..382cfc93bfabf 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/StringExtractOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/StringExtractOperatorTests.java
@@ -41,7 +41,7 @@ public Map<String, String> apply(String s) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         Supplier<Function<String, Map<String, String>>> expEval = () -> new FirstWord("test");
         return new StringExtractOperator.StringExtractOperatorFactory(
             new String[] { "test" },
diff --git a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/topn/TopNOperatorTests.java b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/topn/TopNOperatorTests.java
index bf2f3d2b97dd7..8561ce84744aa 100644
--- a/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/topn/TopNOperatorTests.java
+++ b/x-pack/plugin/esql/compute/src/test/java/org/elasticsearch/compute/operator/topn/TopNOperatorTests.java
@@ -130,7 +130,7 @@ public class TopNOperatorTests extends OperatorTestCase {
     );
 
     @Override
-    protected TopNOperator.TopNOperatorFactory simple() {
+    protected TopNOperator.TopNOperatorFactory simple(SimpleOptions options) {
         return new TopNOperator.TopNOperatorFactory(
             4,
             List.of(LONG),
diff --git a/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/AnyOperatorTestCase.java b/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/AnyOperatorTestCase.java
index 226fb67fdc188..04c2323116ab7 100644
--- a/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/AnyOperatorTestCase.java
+++ b/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/AnyOperatorTestCase.java
@@ -32,11 +32,27 @@
  * Superclass for testing any {@link Operator}, including {@link SourceOperator}s.
  */
 public abstract class AnyOperatorTestCase extends ComputeTestCase {
+    /**
+     * @param requiresDeterministicFactory
+     *          True if the returned {@link Operator.OperatorFactory} should always generate an identical deterministic operator.
+     *          That is, for two different calls, both operators should do "exactly" the same.
+     */
+    protected record SimpleOptions(boolean requiresDeterministicFactory) {
+        public static final SimpleOptions DEFAULT = new SimpleOptions(false);
+    }
+
     /**
      * The operator configured a "simple" or basic way, used for smoke testing
      * descriptions, {@link CircuitBreaker}s, and scatter/gather.
      */
-    protected abstract Operator.OperatorFactory simple();
+    protected abstract Operator.OperatorFactory simple(SimpleOptions options);
+
+    /**
+     * Calls {@link #simple(SimpleOptions)} with the default options.
+     */
+    protected final Operator.OperatorFactory simple() {
+        return simple(SimpleOptions.DEFAULT);
+    }
 
     /**
      * The description of the operator produced by {@link #simple}.
diff --git a/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/OperatorTestCase.java b/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/OperatorTestCase.java
index 0fad56dc99b83..698ae339060db 100644
--- a/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/OperatorTestCase.java
+++ b/x-pack/plugin/esql/compute/test/src/main/java/org/elasticsearch/compute/test/OperatorTestCase.java
@@ -98,7 +98,7 @@ protected ByteSizeValue enoughMemoryForSimple() {
      */
     public final void testSimpleCircuitBreaking() {
         ByteSizeValue memoryLimitForSimple = enoughMemoryForSimple();
-        Operator.OperatorFactory simple = simple();
+        Operator.OperatorFactory simple = simple(new SimpleOptions(true));
         DriverContext inputFactoryContext = driverContext();
         List<Page> input = CannedSourceOperator.collectPages(simpleInput(inputFactoryContext.blockFactory(), between(1_000, 10_000)));
         try {
diff --git a/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/enrich/LookupFromIndexOperatorTests.java b/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/enrich/LookupFromIndexOperatorTests.java
index 87f200da44441..5a9ea4f09ea92 100644
--- a/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/enrich/LookupFromIndexOperatorTests.java
+++ b/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/enrich/LookupFromIndexOperatorTests.java
@@ -123,7 +123,7 @@ protected void assertSimpleOutput(List<Page> input, List<Page> results) {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         String sessionId = "test";
         CancellableTask parentTask = new CancellableTask(0, "test", "test", "test", TaskId.EMPTY_TASK_ID, Map.of());
         int maxOutstandingRequests = 1;
diff --git a/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/inference/RerankOperatorTests.java b/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/inference/RerankOperatorTests.java
index 2833f3fab0d7a..c24602cd74d9b 100644
--- a/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/inference/RerankOperatorTests.java
+++ b/x-pack/plugin/esql/src/test/java/org/elasticsearch/xpack/esql/inference/RerankOperatorTests.java
@@ -88,7 +88,7 @@ public void shutdownThreadPool() {
     }
 
     @Override
-    protected Operator.OperatorFactory simple() {
+    protected Operator.OperatorFactory simple(SimpleOptions options) {
         InferenceRunner inferenceRunner = mockedSimpleInferenceRunner();
         return new RerankOperator.Factory(inferenceRunner, SIMPLE_INFERENCE_ID, SIMPLE_QUERY, rowEncoderFactory, scoreChannel);
     }