diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index c2279d5a8..d466dbac3 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -60,6 +60,9 @@ jobs:
             - os: ubuntu-20.04
               python-version: '3.10'
               toxenv: py310-fuse3
+            - os: ubuntu-20.04
+              python-version: '3.11-dev'
+              toxenv: py311-fuse2
             - os: macos-10.15  # macos-latest is macos 11.6.2 and hanging at test_fuse, #6099
               python-version: '3.8'
               toxenv: py38-fuse2
diff --git a/setup.py b/setup.py
index 84b806b47..5a0e72359 100644
--- a/setup.py
+++ b/setup.py
@@ -67,7 +67,7 @@
 install_requires = [
     # we are rather picky about msgpack versions, because a good working msgpack is
     # very important for borg, see: https://github.com/borgbackup/borg/issues/3753
-    'msgpack >=0.5.6, <=1.0.3, !=1.0.1',
+    'msgpack >=0.5.6, <=1.0.4, !=1.0.1',
     # Please note:
     # using any other version is not supported by borg development and
     # any feedback related to issues caused by this will be ignored.
@@ -285,6 +285,7 @@ def members_appended(*ds):
         'Programming Language :: Python :: 3.8',
         'Programming Language :: Python :: 3.9',
         'Programming Language :: Python :: 3.10',
+        'Programming Language :: Python :: 3.11',
         'Topic :: Security :: Cryptography',
         'Topic :: System :: Archiving :: Backup',
     ],
diff --git a/src/borg/helpers/msgpack.py b/src/borg/helpers/msgpack.py
index 3e2e00a63..3c98b1358 100644
--- a/src/borg/helpers/msgpack.py
+++ b/src/borg/helpers/msgpack.py
@@ -182,7 +182,7 @@ def is_slow_msgpack():
 def is_supported_msgpack():
     # DO NOT CHANGE OR REMOVE! See also requirements and comments in setup.py.
     import msgpack
-    return (0, 5, 6) <= msgpack.version <= (1, 0, 3) and \
+    return (0, 5, 6) <= msgpack.version <= (1, 0, 4) and \
            msgpack.version not in [(1, 0, 1), ]  # < add bad releases here to deny list
 
 
diff --git a/tox.ini b/tox.ini
index f23ae78d2..0f727bf98 100644
--- a/tox.ini
+++ b/tox.ini
@@ -2,7 +2,7 @@
 # fakeroot -u tox --recreate
 
 [tox]
-envlist = py{38,39,310}-{none,fuse2,fuse3}
+envlist = py{38,39,310,311}-{none,fuse2,fuse3}
 minversion = 3.2
 requires =
 	pkgconfig