diff --git a/streams/src/main/java/org/apache/kafka/streams/processor/assignment/assignors/StickyTaskAssignor.java b/streams/src/main/java/org/apache/kafka/streams/processor/assignment/assignors/StickyTaskAssignor.java
index 6ad61851ddae3..60c715fea4f3b 100644
--- a/streams/src/main/java/org/apache/kafka/streams/processor/assignment/assignors/StickyTaskAssignor.java
+++ b/streams/src/main/java/org/apache/kafka/streams/processor/assignment/assignors/StickyTaskAssignor.java
@@ -146,7 +146,6 @@ private static void assignActive(final ApplicationState applicationState,
         final int totalCapacity = computeTotalProcessingThreads(clients);
         final Set<TaskId> allTaskIds = applicationState.allTasks().keySet();
         final int taskCount = allTaskIds.size();
-        final int activeTasksPerThread = taskCount / totalCapacity;
         final Set<TaskId> unassigned = new HashSet<>(allTaskIds);
 
         // first try and re-assign existing active tasks to clients that previously had
@@ -154,7 +153,7 @@ private static void assignActive(final ApplicationState applicationState,
         for (final TaskId taskId : assignmentState.previousActiveAssignment.keySet()) {
             final ProcessId previousClientForTask = assignmentState.previousActiveAssignment.get(taskId);
             if (allTaskIds.contains(taskId)) {
-                if (mustPreserveActiveTaskAssignment || assignmentState.hasRoomForActiveTask(previousClientForTask, activeTasksPerThread)) {
+                if (mustPreserveActiveTaskAssignment || assignmentState.hasRoomForActiveTask(previousClientForTask, taskCount, totalCapacity)) {
                     assignmentState.finalizeAssignment(taskId, previousClientForTask, AssignedTask.Type.ACTIVE);
                     unassigned.remove(taskId);
                 }
@@ -167,7 +166,7 @@ private static void assignActive(final ApplicationState applicationState,
             final TaskId taskId = iterator.next();
             final Set<ProcessId> previousClientsForStandbyTask = assignmentState.previousStandbyAssignment.getOrDefault(taskId, new HashSet<>());
             for (final ProcessId client: previousClientsForStandbyTask) {
-                if (assignmentState.hasRoomForActiveTask(client, activeTasksPerThread)) {
+                if (assignmentState.hasRoomForActiveTask(client, taskCount, totalCapacity)) {
                     assignmentState.finalizeAssignment(taskId, client, AssignedTask.Type.ACTIVE);
                     iterator.remove();
                     break;
@@ -295,14 +294,15 @@ private void processOptimizedAssignments(final Map<ProcessId, KafkaStreamsAssign
             this.newAssignments = optimizedAssignments;
         }
 
-        private boolean hasRoomForActiveTask(final ProcessId processId, final int activeTasksPerThread) {
+        private boolean hasRoomForActiveTask(final ProcessId processId, final int taskCount, final int totalCapacity) {
             final int capacity = clients.get(processId).numProcessingThreads();
             final int newActiveTaskCount = newAssignments.computeIfAbsent(processId, k -> KafkaStreamsAssignment.of(processId, new HashSet<>()))
                 .tasks().values()
                 .stream().filter(assignedTask -> assignedTask.type() == AssignedTask.Type.ACTIVE)
                 .collect(Collectors.toSet())
                 .size();
-            return newActiveTaskCount < capacity * activeTasksPerThread;
+            final int instanceLimit = (taskCount * capacity + totalCapacity - 1) / totalCapacity;
+            return newActiveTaskCount < instanceLimit;
         }
 
         private ProcessId findBestClientForTask(final TaskId taskId, final Set<ProcessId> clientsWithin) {
diff --git a/streams/src/test/java/org/apache/kafka/streams/processor/internals/assignment/CustomStickyTaskAssignorTest.java b/streams/src/test/java/org/apache/kafka/streams/processor/internals/assignment/CustomStickyTaskAssignorTest.java
index fa92a55dcae4c..a417926b50288 100644
--- a/streams/src/test/java/org/apache/kafka/streams/processor/internals/assignment/CustomStickyTaskAssignorTest.java
+++ b/streams/src/test/java/org/apache/kafka/streams/processor/internals/assignment/CustomStickyTaskAssignorTest.java
@@ -39,6 +39,8 @@
 import java.util.ArrayList;
 import java.util.Collection;
 import java.util.Collections;
+import java.util.HashMap;
+import java.util.HashSet;
 import java.util.List;
 import java.util.Map;
 import java.util.Optional;
@@ -69,6 +71,7 @@
 import static org.apache.kafka.streams.processor.internals.assignment.TaskAssignmentUtilsTest.mkStreamState;
 import static org.apache.kafka.streams.processor.internals.assignment.TaskAssignmentUtilsTest.mkTaskInfo;
 import static org.apache.kafka.streams.processor.internals.assignment.TaskAssignmentUtilsTest.processId;
+import static org.junit.jupiter.api.Assertions.fail;
 import static org.hamcrest.MatcherAssert.assertThat;
 import static org.hamcrest.Matchers.equalTo;
 import static org.hamcrest.Matchers.greaterThanOrEqualTo;
@@ -913,4 +916,78 @@ private void assertActiveTaskTopicGroupIdsEvenlyDistributed(final Map<ProcessId,
             assertThat(topicGroupIds, equalTo(asList(1, 2)));
         }
     }
+
+    // --- KAFKA-20198 regression tests ---
+
+    @Test
+    public void shouldRetainFairShareOfPreviousTasksWhenScalingUp() {
+        final int numTasks = 450;
+        final int threadsPerInstance = 10;
+        final Map<TaskId, TaskInfo> tasks = buildStatelessTasks(numTasks);
+        final Set<TaskId> firstHalf = buildTaskIdRange(0, numTasks / 2);
+
+        final Map<ProcessId, KafkaStreamsState> streamStates = mkMap(
+            mkStreamState(1, threadsPerInstance, Optional.empty(), firstHalf, Set.of()),
+            mkStreamState(2, threadsPerInstance, Optional.empty())
+        );
+
+        final Map<ProcessId, KafkaStreamsAssignment> assignments =
+            assign(streamStates, tasks, StreamsConfig.RACK_AWARE_ASSIGNMENT_STRATEGY_NONE);
+
+        final Set<TaskId> instance1Tasks = activeTasks(assignments, 1);
+        final int retained = (int) firstHalf.stream().filter(instance1Tasks::contains).count();
+
+        assertThat("Instance should retain all of its fair share tasks, but only retained " + retained + " of " + firstHalf.size(),
+            retained, equalTo(firstHalf.size()));
+    }
+
+    @Test
+    public void shouldConvergeWithinTwoRoundsWhenScalingUp() {
+        // Reporter's scenario: 450 tasks with 10+10=20 threads.
+        // 450/20 = 22.5, floor gives limit 220 per instance (10 task overflow),
+        // causing repeated reassignment across rounds.
+        final int numTasks = 450;
+        final int maxRounds = 2;
+        final Map<TaskId, TaskInfo> tasks = buildStatelessTasks(numTasks);
+
+        Set<TaskId> instance1Prev = buildTaskIdRange(0, numTasks);
+        Set<TaskId> instance2Prev = Set.of();
+
+        for (int round = 1; round <= maxRounds; round++) {
+            final Map<ProcessId, KafkaStreamsState> streamStates = mkMap(
+                mkStreamState(1, 10, Optional.empty(), instance1Prev, Set.of()),
+                mkStreamState(2, 10, Optional.empty(), instance2Prev, Set.of())
+            );
+
+            final Map<ProcessId, KafkaStreamsAssignment> assignments =
+                assign(streamStates, tasks, StreamsConfig.RACK_AWARE_ASSIGNMENT_STRATEGY_NONE);
+
+            final Set<TaskId> newInstance1 = activeTasks(assignments, 1);
+            final Set<TaskId> newInstance2 = activeTasks(assignments, 2);
+
+            if (newInstance1.equals(instance1Prev) && newInstance2.equals(instance2Prev)) {
+                return; // converged
+            }
+            instance1Prev = newInstance1;
+            instance2Prev = newInstance2;
+        }
+        fail("Assignment did not converge within " + maxRounds + " rounds");
+    }
+
+    private static Map<TaskId, TaskInfo> buildStatelessTasks(final int count) {
+        final Map<TaskId, TaskInfo> tasks = new HashMap<>();
+        for (int i = 0; i < count; i++) {
+            final TaskId taskId = new TaskId(0, i);
+            tasks.put(taskId, mkTaskInfo(taskId, false).getValue());
+        }
+        return tasks;
+    }
+
+    private static Set<TaskId> buildTaskIdRange(final int from, final int to) {
+        final Set<TaskId> set = new HashSet<>();
+        for (int i = from; i < to; i++) {
+            set.add(new TaskId(0, i));
+        }
+        return set;
+    }
 }