diff --git a/fsspec/caching.py b/fsspec/caching.py
index 34231c881..3be267626 100644
--- a/fsspec/caching.py
+++ b/fsspec/caching.py
@@ -37,6 +37,7 @@
 logger = logging.getLogger("fsspec")
 
 Fetcher = Callable[[int, int], bytes]  # Maps (start, end) to bytes
+MultiFetcher = Callable[list[[int, int]], bytes]  # Maps [(start, end)] to bytes
 
 
 class BaseCache:
@@ -109,6 +110,26 @@ class MMapCache(BaseCache):
     Ensure there is enough disc space in the temporary location.
 
     This cache method might only work on posix
+
+    Parameters
+    ----------
+    blocksize: int
+        How far to read ahead in numbers of bytes
+    fetcher: Fetcher
+        Function of the form f(start, end) which gets bytes from remote as
+        specified
+    size: int
+        How big this file is
+    location: str
+        Where to create the temporary file. If None, a temporary file is
+        created using tempfile.TemporaryFile().
+    blocks: set[int]
+        Set of block numbers that have already been fetched. If None, an empty
+        set is created.
+    multi_fetcher: MultiFetcher
+        Function of the form f([(start, end)]) which gets bytes from remote
+        as specified. This function is used to fetch multiple blocks at once.
+        If not specified, the fetcher function is used instead.
     """
 
     name = "mmap"
@@ -120,10 +141,12 @@ def __init__(
         size: int,
         location: str | None = None,
         blocks: set[int] | None = None,
+        multi_fetcher: MultiFetcher | None = None,
     ) -> None:
         super().__init__(blocksize, fetcher, size)
         self.blocks = set() if blocks is None else blocks
         self.location = location
+        self.multi_fetcher = multi_fetcher
         self.cache = self._makefile()
 
     def _makefile(self) -> mmap.mmap | bytearray:
@@ -164,6 +187,8 @@ def _fetch(self, start: int | None, end: int | None) -> bytes:
         # Count the number of blocks already cached
         self.hit_count += sum(1 for i in block_range if i in self.blocks)
 
+        ranges = []
+
         # Consolidate needed blocks.
         # Algorithm adapted from Python 2.x itertools documentation.
         # We are grouping an enumerated sequence of blocks. By comparing when the difference
@@ -185,13 +210,27 @@ def _fetch(self, start: int | None, end: int | None) -> bytes:
             logger.debug(
                 f"MMap get blocks {_blocks[0]}-{_blocks[-1]} ({sstart}-{send})"
             )
-            self.cache[sstart:send] = self.fetcher(sstart, send)
+            ranges.append((sstart, send))
 
             # Update set of cached blocks
             self.blocks.update(_blocks)
             # Update cache statistics with number of blocks we had to cache
             self.miss_count += len(_blocks)
 
+        if not ranges:
+            return self.cache[start:end]
+
+        if self.multi_fetcher:
+            logger.debug(f"MMap get blocks {ranges}")
+            for idx, r in enumerate(self.multi_fetcher(ranges)):
+                (sstart, send) = ranges[idx]
+                logger.debug(f"MMap copy block ({sstart}-{send}")
+                self.cache[sstart:send] = r
+        else:
+            for sstart, send in ranges:
+                logger.debug(f"MMap get block ({sstart}-{send}")
+                self.cache[sstart:send] = self.fetcher(sstart, send)
+
         return self.cache[start:end]
 
     def __getstate__(self) -> dict[str, Any]:
diff --git a/fsspec/implementations/cached.py b/fsspec/implementations/cached.py
index 8b8b83295..bd58ad496 100644
--- a/fsspec/implementations/cached.py
+++ b/fsspec/implementations/cached.py
@@ -362,7 +362,19 @@ def _open(
                 )
         else:
             detail["blocksize"] = f.blocksize
-        f.cache = MMapCache(f.blocksize, f._fetch_range, f.size, fn, blocks)
+
+        def _fetch_ranges(ranges):
+            return self.fs.cat_ranges(
+                [path] * len(ranges),
+                [r[0] for r in ranges],
+                [r[1] for r in ranges],
+                **kwargs,
+            )
+
+        multi_fetcher = None if self.compression else _fetch_ranges
+        f.cache = MMapCache(
+            f.blocksize, f._fetch_range, f.size, fn, blocks, multi_fetcher=multi_fetcher
+        )
         close = f.close
         f.close = lambda: self.close_and_update(f, close)
         self.save_cache()
diff --git a/fsspec/tests/test_caches.py b/fsspec/tests/test_caches.py
index 6176d8001..5299a0824 100644
--- a/fsspec/tests/test_caches.py
+++ b/fsspec/tests/test_caches.py
@@ -6,6 +6,7 @@
 from fsspec.caching import (
     BlockCache,
     FirstChunkCache,
+    MMapCache,
     ReadAheadCache,
     caches,
     register_cache,
@@ -147,6 +148,10 @@ def letters_fetcher(start, end):
     return string.ascii_letters[start:end].encode()
 
 
+def multi_letters_fetcher(ranges):
+    return [string.ascii_letters[start:end].encode() for start, end in ranges]
+
+
 not_parts_caches = {k: v for k, v in caches.items() if k != "parts"}
 
 
@@ -174,6 +179,38 @@ def test_cache_pickleable(Cache_imp):
     assert unpickled._fetch(0, 10) == b"0" * 10
 
 
+def test_first_cache():
+    c = FirstChunkCache(5, letters_fetcher, 52)
+    assert c.cache is None
+    assert c._fetch(12, 15) == letters_fetcher(12, 15)
+    assert c.cache is None
+    assert c._fetch(3, 10) == letters_fetcher(3, 10)
+    assert c.cache == letters_fetcher(0, 5)
+    c.fetcher = None
+    assert c._fetch(1, 4) == letters_fetcher(1, 4)
+
+
+def test_mmap_cache(mocker):
+    fetcher = mocker.Mock(wraps=letters_fetcher)
+    c = MMapCache(5, fetcher, 52)
+    assert c._fetch(6, 8) == letters_fetcher(6, 8)
+    assert fetcher.call_count == 1
+    assert c._fetch(17, 22) == letters_fetcher(17, 22)
+    assert fetcher.call_count == 2
+    assert c._fetch(1, 38) == letters_fetcher(1, 38)
+    assert fetcher.call_count == 5
+
+    multi_fetcher = mocker.Mock(wraps=multi_letters_fetcher)
+    m = MMapCache(5, fetcher, size=52, multi_fetcher=multi_fetcher)
+    assert m._fetch(6, 8) == letters_fetcher(6, 8)
+    assert multi_fetcher.call_count == 1
+    assert m._fetch(17, 22) == letters_fetcher(17, 22)
+    assert multi_fetcher.call_count == 2
+    assert m._fetch(1, 38) == letters_fetcher(1, 38)
+    assert multi_fetcher.call_count == 3
+    assert fetcher.call_count == 5
+
+
 @pytest.mark.parametrize(
     "size_requests",
     [[(0, 30), (0, 35), (51, 52)], [(0, 1), (1, 11), (1, 52)], [(0, 52), (11, 15)]],