diff --git a/tests/conftest.py b/tests/conftest.py
index 67845d32..1e2e7981 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -32,6 +32,7 @@ def jp_server_config(jp_root_dir, jp_server_config):
             "password": "",
             "disable_check_xsrf": True,
         },
+        "YDocExtension": {"document_cleanup_delay": 0},
         "SQLiteYStore": {"db_path": str(jp_root_dir.joinpath(".rtc_test.db"))},
         "BaseFileIdManager": {
             "root_dir": str(jp_root_dir),
@@ -90,6 +91,8 @@ async def _inner(
         # Create a notebook string and write to file.
         if content is None:
             nb = nbformat.v4.new_notebook()
+            notary = nbformat.sign.NotebookNotary()
+            notary.sign(nb)
             content = nbformat.writes(nb, version=4)
 
         nbpath.write_text(content)
diff --git a/tests/test_app.py b/tests/test_app.py
index becc278c..37856ca5 100644
--- a/tests/test_app.py
+++ b/tests/test_app.py
@@ -11,7 +11,7 @@ def test_default_settings(jp_serverapp):
 
     assert settings["disable_rtc"] is False
     assert settings["file_poll_interval"] == 1
-    assert settings["document_cleanup_delay"] == 60
+    assert settings["document_cleanup_delay"] == 0
     assert settings["document_save_delay"] == 1
     assert settings["ystore_class"] == SQLiteYStore
 
diff --git a/tests/test_general.py b/tests/test_general.py
new file mode 100644
index 00000000..188a1d27
--- /dev/null
+++ b/tests/test_general.py
@@ -0,0 +1,142 @@
+# Copyright (c) Jupyter Development Team.
+# Distributed under the terms of the Modified BSD License.
+
+from __future__ import annotations
+
+from asyncio import Event, create_task, sleep, wait
+from typing import Any
+
+import nbformat
+from jupyter_ydoc import YNotebook, YUnicode
+from ypy_websocket import WebsocketProvider
+
+
+async def test_clients(rtc_create_file, rtc_connect_doc_client):
+    file_path = "test.txt"
+    file_format = "text"
+    file_type = "file"
+    await rtc_create_file(file_path)
+
+    async def fn(
+        format: str, type: str, path: str, doc: YUnicode, content: int | None = None
+    ) -> None:
+
+        event = Event()
+
+        def callback(e: Any) -> None:
+            nonlocal event
+            event.set()
+
+        test_array = doc.ydoc.get_array("test")
+        test_array.observe(callback)
+
+        async with await rtc_connect_doc_client(format, type, path) as ws, WebsocketProvider(
+            doc.ydoc, ws
+        ):
+            if content is not None:
+                with doc.ydoc.begin_transaction() as txn:
+                    test_array.extend(txn, [content])
+                await event.wait()
+            await sleep(0.1)
+
+    clients = []
+    n = 10
+    for _ in range(n):
+        doc = YUnicode()
+        clients.append(create_task(fn(file_format, file_type, file_path, doc, 1)))
+
+    doc = YUnicode()
+    test_array = doc.ydoc.get_array("test")
+    clients.append(create_task(fn(file_format, file_type, file_path, doc)))
+
+    await wait(clients)
+
+    assert sum(list(test_array)) == n
+    await sleep(1)
+
+
+async def test_clients_insert_text(rtc_create_file, rtc_connect_doc_client):
+    file_path = "test.txt"
+    file_format = "text"
+    file_type = "file"
+    await rtc_create_file(file_path)
+
+    async def fn(
+        format: str, type: str, path: str, doc: YUnicode, content: str | None = None
+    ) -> None:
+        event = Event()
+
+        def callback(target: str, e: Any) -> None:
+            nonlocal event
+            if target == "source":
+                event.set()
+
+        doc.observe(callback)
+
+        async with await rtc_connect_doc_client(format, type, path) as ws, WebsocketProvider(
+            doc.ydoc, ws
+        ):
+            if content is not None:
+                with doc.ydoc.begin_transaction() as txn:
+                    doc._ysource.extend(txn, content)
+                await event.wait()
+            await sleep(0.1)
+
+    n = 10
+    content = "test"
+    res = len(content) * n
+
+    clients = []
+    for _ in range(n):
+        doc = YUnicode()
+        clients.append(create_task(fn(file_format, file_type, file_path, doc, content)))
+
+    doc = YUnicode()
+    clients.append(create_task(fn(file_format, file_type, file_path, doc)))
+
+    await wait(clients)
+
+    assert len(doc._ysource) == res
+    await sleep(1)
+
+
+async def test_clients_insert_cell(rtc_create_notebook, rtc_connect_doc_client):
+    file_path = "test.ipynb"
+    file_format = "json"
+    file_type = "notebook"
+    await rtc_create_notebook(file_path)
+
+    async def fn(
+        format: str, type: str, path: str, doc: YNotebook, content: str | None = ""
+    ) -> None:
+        event = Event()
+
+        def callback(target: str, e: Any) -> None:
+            nonlocal event
+            if target == "cells":
+                event.set()
+
+        doc.observe(callback)
+
+        async with await rtc_connect_doc_client(format, type, path) as ws, WebsocketProvider(
+            doc.ydoc, ws
+        ):
+            if content is not None:
+                doc.append_cell(nbformat.v4.new_code_cell(content))
+                await event.wait()
+            await sleep(0.1)
+
+    n = 10
+    clients = []
+    for _ in range(n):
+        doc = YNotebook()
+        clients.append(create_task(fn(file_format, file_type, file_path, doc, "test")))
+
+    doc = YNotebook()
+    clients.append(create_task(fn(file_format, file_type, file_path, doc, None)))
+
+    await wait(clients)
+
+    # +1 For the initial cell :(
+    assert doc.cell_number == n + 1
+    await sleep(1)