diff --git a/nbclient/client.py b/nbclient/client.py
index b2a1d07..9ad710b 100644
--- a/nbclient/client.py
+++ b/nbclient/client.py
@@ -4,6 +4,7 @@
 import base64
 import collections
 import datetime
+import re
 import signal
 import typing as t
 from contextlib import asynccontextmanager, contextmanager
@@ -28,6 +29,9 @@
 from .output_widget import OutputWidget
 from .util import ensure_async, run_hook, run_sync
 
+_RGX_CARRIAGERETURN = re.compile(r".*\r(?=[^\n])")
+_RGX_BACKSPACE = re.compile(r"[^\n]\b")
+
 
 def timestamp(msg: t.Optional[t.Dict] = None) -> str:
     """Get the timestamp for a message."""
@@ -426,6 +430,14 @@ def _kernel_manager_class_default(self) -> t.Type[KernelManager]:
         )
     )
 
+    coalesce_streams = Bool(
+        help=dedent(
+            """
+            Merge all stream outputs with shared names into single streams.
+            """
+        )
+    )
+
     def __init__(self, nb: NotebookNode, km: t.Optional[KernelManager] = None, **kw: t.Any) -> None:
         """Initializes the execution manager.
 
@@ -1006,6 +1018,44 @@ async def async_execute_cell(
             self.on_cell_executed, cell=cell, cell_index=cell_index, execute_reply=exec_reply
         )
         await self._check_raise_for_error(cell, cell_index, exec_reply)
+
+        if self.coalesce_streams and cell.outputs:
+            new_outputs = []
+            streams: dict[str, NotebookNode] = {}
+            for output in cell.outputs:
+                if output["output_type"] == "stream":
+                    if output["name"] in streams:
+                        streams[output["name"]]["text"] += output["text"]
+                    else:
+                        new_outputs.append(output)
+                        streams[output["name"]] = output
+                else:
+                    new_outputs.append(output)
+
+            # process \r and \b characters
+            for output in streams.values():
+                old = output["text"]
+                while len(output["text"]) < len(old):
+                    old = output["text"]
+                    # Cancel out anything-but-newline followed by backspace
+                    output["text"] = _RGX_BACKSPACE.sub("", output["text"])
+                # Replace all carriage returns not followed by newline
+                output["text"] = _RGX_CARRIAGERETURN.sub("", output["text"])
+
+            # We also want to ensure stdout and stderr are always in the same consecutive order,
+            # because they are asynchronous, so order isn't guaranteed.
+            for i, output in enumerate(new_outputs):
+                if output["output_type"] == "stream" and output["name"] == "stderr":
+                    if (
+                        len(new_outputs) >= i + 2
+                        and new_outputs[i + 1]["output_type"] == "stream"
+                        and new_outputs[i + 1]["name"] == "stdout"
+                    ):
+                        stdout = new_outputs.pop(i + 1)
+                        new_outputs.insert(i, stdout)
+
+            cell.outputs = new_outputs
+
         self.nb['cells'][cell_index] = cell
         return cell
 
diff --git a/nbclient/tests/test_client.py b/nbclient/tests/test_client.py
index 0c75698..946cc33 100644
--- a/nbclient/tests/test_client.py
+++ b/nbclient/tests/test_client.py
@@ -1830,3 +1830,34 @@ def test_error_async_cell_hooks(self, executor, cell_mock, message_mock):
         hooks["on_notebook_start"].assert_not_called()
         hooks["on_notebook_complete"].assert_not_called()
         hooks["on_notebook_error"].assert_not_called()
+
+    @prepare_cell_mocks(
+        {
+            'msg_type': 'stream',
+            'header': {'msg_type': 'stream'},
+            'content': {'name': 'stdout', 'text': 'foo1'},
+        },
+        {
+            'msg_type': 'stream',
+            'header': {'msg_type': 'stream'},
+            'content': {'name': 'stderr', 'text': 'bar1'},
+        },
+        {
+            'msg_type': 'stream',
+            'header': {'msg_type': 'stream'},
+            'content': {'name': 'stdout', 'text': 'foo2'},
+        },
+        {
+            'msg_type': 'stream',
+            'header': {'msg_type': 'stream'},
+            'content': {'name': 'stderr', 'text': 'bar2'},
+        },
+    )
+    def test_coalesce_streams(self, executor, cell_mock, message_mock):
+        executor.coalesce_streams = True
+        executor.execute_cell(cell_mock, 0)
+
+        assert cell_mock.outputs == [
+            {'output_type': 'stream', 'name': 'stdout', 'text': 'foo1foo2'},
+            {'output_type': 'stream', 'name': 'stderr', 'text': 'bar1bar2'},
+        ]