diff --git a/distributed/comm/tcp.py b/distributed/comm/tcp.py
index 774d606e2a1..c741aba83e9 100644
--- a/distributed/comm/tcp.py
+++ b/distributed/comm/tcp.py
@@ -44,14 +44,14 @@
 logger = logging.getLogger(__name__)
 
 
-# Workaround for OpenSSL 1.0.2.
-# Can drop with OpenSSL 1.1.1 used by Python 3.10+.
-# ref: https://bugs.python.org/issue42853
-if sys.version_info < (3, 10):
-    OPENSSL_MAX_CHUNKSIZE = 256 ** ctypes.sizeof(ctypes.c_int) // 2 - 1
-else:
-    OPENSSL_MAX_CHUNKSIZE = 256 ** ctypes.sizeof(ctypes.c_size_t) - 1
-
+# We must not load more than this into a buffer at a time
+# It's currently unclear why that is
+# see
+# - https://github.com/dask/distributed/pull/5854
+# - https://bugs.python.org/issue42853
+# - https://github.com/dask/distributed/pull/8507
+
+C_INT_MAX = 256 ** ctypes.sizeof(ctypes.c_int) // 2 - 1
 MAX_BUFFER_SIZE = MEMORY_LIMIT / 2
 
 
@@ -286,8 +286,8 @@ async def write(self, msg, serializers=None, on_error="message"):
                         2,
                         range(
                             0,
-                            each_frame_nbytes + OPENSSL_MAX_CHUNKSIZE,
-                            OPENSSL_MAX_CHUNKSIZE,
+                            each_frame_nbytes + C_INT_MAX,
+                            C_INT_MAX,
                         ),
                     ):
                         chunk = each_frame[i:j]
@@ -360,7 +360,7 @@ async def read_bytes_rw(stream: IOStream, n: int) -> memoryview:
 
     for i, j in sliding_window(
         2,
-        range(0, n + OPENSSL_MAX_CHUNKSIZE, OPENSSL_MAX_CHUNKSIZE),
+        range(0, n + C_INT_MAX, C_INT_MAX),
     ):
         chunk = buf[i:j]
         actual = await stream.read_into(chunk)  # type: ignore[arg-type]
@@ -432,7 +432,8 @@ class TLS(TCP):
     A TLS-specific version of TCP.
     """
 
-    max_shard_size = min(OPENSSL_MAX_CHUNKSIZE, TCP.max_shard_size)
+    # Workaround for OpenSSL 1.0.2 (can drop with OpenSSL 1.1.1)
+    max_shard_size = min(C_INT_MAX, TCP.max_shard_size)
 
     def _read_extra(self):
         TCP._read_extra(self)
diff --git a/distributed/protocol/tests/test_protocol.py b/distributed/protocol/tests/test_protocol.py
index 630239c1adc..c9db26fb79c 100644
--- a/distributed/protocol/tests/test_protocol.py
+++ b/distributed/protocol/tests/test_protocol.py
@@ -208,3 +208,30 @@ def test_fallback_to_pickle():
     assert L[0].count(b"__Pickled__") == 1
     assert L[0].count(b"__Serialized__") == 1
     assert loads(L) == {np.int64(1): {2: "a"}, 3: ("b", "c"), 4: "d"}
+
+
+@pytest.mark.slow
+@pytest.mark.parametrize("typ", [bytes, str, "ext"])
+def test_large_payload(typ):
+    """See also: test_core.py::test_large_payload"""
+    critical_size = 2**31 + 1  # >2 GiB
+    if typ == bytes:
+        large_payload = critical_size * b"0"
+        expected = large_payload
+    elif typ == str:
+        large_payload = critical_size * "0"
+        expected = large_payload
+    # Testing array and map dtypes is practically not possible since we'd have
+    # to create an actual list or dict object of critical size (i.e. not the
+    # content but the container itself). These are so large that msgpack is
+    # running forever
+    # elif typ == "array":
+    #     large_payload = [b"0"] * critical_size
+    #     expected = tuple(large_payload)
+    # elif typ == "map":
+    #     large_payload = {x: b"0" for x in range(critical_size)}
+    #     expected = large_payload
+    elif typ == "ext":
+        large_payload = msgpack.ExtType(1, b"0" * critical_size)
+        expected = large_payload
+    assert loads(dumps(large_payload)) == expected
diff --git a/distributed/protocol/utils.py b/distributed/protocol/utils.py
index f7fa7a9984a..0777b8f9e0d 100644
--- a/distributed/protocol/utils.py
+++ b/distributed/protocol/utils.py
@@ -12,9 +12,7 @@
 BIG_BYTES_SHARD_SIZE = dask.utils.parse_bytes(dask.config.get("distributed.comm.shard"))
 
 
-msgpack_opts = {
-    ("max_%s_len" % x): 2**31 - 1 for x in ["str", "bin", "array", "map", "ext"]
-}
+msgpack_opts = {}
 msgpack_opts["strict_map_key"] = False
 msgpack_opts["raw"] = False
 
diff --git a/distributed/tests/test_core.py b/distributed/tests/test_core.py
index 85a502bafee..93bb18f16d3 100644
--- a/distributed/tests/test_core.py
+++ b/distributed/tests/test_core.py
@@ -2,6 +2,7 @@
 
 import asyncio
 import contextlib
+import logging
 import os
 import random
 import socket
@@ -1481,3 +1482,27 @@ def sync_handler(val):
             assert ledger == list(range(n))
         finally:
             await comm.close()
+
+
+@pytest.mark.slow
+@gen_test(timeout=180)
+async def test_large_payload(caplog):
+    """See also: protocol/tests/test_protocol.py::test_large_payload"""
+    critical_size = 2**31 + 1  # >2 GiB
+    data = b"0" * critical_size
+
+    async with Server({"echo": echo_serialize}) as server:
+        await server.listen(0)
+        comm = await connect(server.address)
+
+        # FIXME https://github.com/dask/distributed/issues/8465
+        # At debug level, messages are dumped into the log. By default, pytest captures
+        # all logs, which would make this test extremely expensive to run.
+        with caplog.at_level(logging.INFO, logger="distributed.core"):
+            # Note: if we wrap data in to_serialize, it will be sent as a buffer, which
+            # is not encoded by msgpack.
+            await comm.write({"op": "echo", "x": data})
+            response = await comm.read()
+
+        assert response["result"] == data
+        await comm.close()