diff --git a/CHANGELOG.md b/CHANGELOG.md
index ddb1a8fa..f40df2eb 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -6,6 +6,7 @@ See Git checking messages for full history.
 - added support for Python 3.13
 - leveled up the packaging using `hatchling`
 - used `ruff` to lint the code base (#275)
+- MSS: allow to use a custom date function for output file names (#276)
 - MSS: minor optimization when using an output file format without date (#275)
 - MSS: fixed `Pixel` model type (#274)
 - CI: automated release publishing on tag creation
diff --git a/docs/source/api.rst b/docs/source/api.rst
index cef76dab..d297968a 100644
--- a/docs/source/api.rst
+++ b/docs/source/api.rst
@@ -168,12 +168,16 @@ Methods
             *monitor* can be a ``tuple`` like ``PIL.Image.grab()`` accepts,
             it will be converted to the appropriate ``dict``.
 
-    .. method:: save([mon=1], [output='mon-{mon}.png'], [callback=None])
+    .. method:: save([mon=1], [output='mon-{mon}.png'], [callback=None], [date_fn=None])
 
         :param int mon: the monitor's number.
         :param str output: the output's file name.
         :type callback: callable or None
         :param callback: callback called before saving the screen shot to a file. Takes the *output* argument as parameter.
+        :type callback: callable or None
+        :param callback: callback called before saving the screen shot to a file. Takes the *output* argument as parameter.
+        Function returning a `datetime` object,
+            used to format the date in output file names.
         :rtype: iterable
         :return: Created file(s).
 
diff --git a/pyproject.toml b/pyproject.toml
index c8065c39..b3cce0f3 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -71,6 +71,7 @@ mss = "mss.__main__:main"
 
 [project.optional-dependencies]
 test = [
+  "freezegun",
   "numpy ; sys_platform == 'windows' and python_version >= '3.13'",
   "pillow",
   "pytest",
diff --git a/src/mss/base.py b/src/mss/base.py
index 4438693f..a2cb5236 100644
--- a/src/mss/base.py
+++ b/src/mss/base.py
@@ -29,6 +29,10 @@
 lock = Lock()
 
 
+def date_function() -> datetime:
+    return datetime.now(UTC)
+
+
 class MSSBase(metaclass=ABCMeta):
     """This class will be overloaded by a system specific one."""
 
@@ -131,6 +135,7 @@ def save(
         mon: int = 0,
         output: str = "monitor-{mon}.png",
         callback: Callable[[str], None] | None = None,
+        date_fn: Callable[[], datetime] = date_function,
     ) -> Iterator[str]:
         """Grab a screen shot and save it to a file.
 
@@ -154,6 +159,8 @@ def save(
 
         :param callable callback: Callback called before saving the
             screen shot to a file.  Take the `output` argument as parameter.
+        :param callable date_fn: Function returning a `datetime` object,
+            used to format the date in output file names.
 
         :return generator: Created file(s).
         """
@@ -165,7 +172,7 @@ def save(
         if mon == 0:
             # One screen shot by monitor
             for idx, monitor in enumerate(monitors[1:], 1):
-                fname = output.format(mon=idx, date=datetime.now(UTC) if "{date" in output else None, **monitor)
+                fname = output.format(mon=idx, date=date_fn() if "{date" in output else None, **monitor)
                 if callable(callback):
                     callback(fname)
                 sct = self.grab(monitor)
@@ -181,7 +188,7 @@ def save(
                 msg = f"Monitor {mon!r} does not exist."
                 raise ScreenShotError(msg) from exc
 
-            output = output.format(mon=mon, date=datetime.now(UTC) if "{date" in output else None, **monitor)
+            output = output.format(mon=mon, date=date_fn() if "{date" in output else None, **monitor)
             if callable(callback):
                 callback(output)
             sct = self.grab(monitor)
diff --git a/src/tests/test_save.py b/src/tests/test_save.py
index 3ae0f6f8..2f50e80a 100644
--- a/src/tests/test_save.py
+++ b/src/tests/test_save.py
@@ -3,9 +3,10 @@
 """
 
 import os.path
-from datetime import datetime
+from datetime import datetime, timedelta
 
 import pytest
+from freezegun import freeze_time
 from mss import mss
 
 try:
@@ -17,6 +18,9 @@
     UTC = timezone.utc
 
 
+FROZEN_TIME = "2024-02-21 16:35:20"
+
+
 def test_at_least_2_monitors() -> None:
     with mss(display=os.getenv("DISPLAY")) as sct:
         assert list(sct.save(mon=0))
@@ -79,3 +83,27 @@ def test_output_format_date_custom() -> None:
         filename = sct.shot(mon=1, output=fmt)
     assert filename == fmt.format(date=datetime.now(tz=UTC))
     assert os.path.isfile(filename)
+
+
+@freeze_time(FROZEN_TIME)
+def test_output_format_custom_date_function() -> None:
+    def custom_date() -> datetime:
+        return datetime.now(tz=UTC) + timedelta(days=6)
+
+    fmt = "{date}.png"
+    with mss(display=os.getenv("DISPLAY")) as sct:
+        filename = sct.shot(mon=1, output=fmt, date_fn=custom_date)
+    assert filename == "2024-02-27 16:35:20+00:00.png"
+    assert os.path.isfile(filename)
+
+
+@freeze_time(FROZEN_TIME)
+def test_output_format_date_custom_and_custom_date_function() -> None:
+    def custom_date() -> datetime:
+        return datetime.now(tz=UTC) + timedelta(days=6)
+
+    fmt = "{date:%Y-%m-%d}.png"
+    with mss(display=os.getenv("DISPLAY")) as sct:
+        filename = sct.shot(mon=1, output=fmt, date_fn=custom_date)
+    assert filename == "2024-02-27.png"
+    assert os.path.isfile(filename)