diff --git a/.github/workflows/build-test.yml b/.github/workflows/build-test.yml
index 16173cf9..ec28562b 100644
--- a/.github/workflows/build-test.yml
+++ b/.github/workflows/build-test.yml
@@ -17,15 +17,16 @@ jobs:
       fail-fast: false  # need to see which ones fail
       matrix:
         os: [ubuntu-latest, windows-latest, macos-latest]
-        python: ["3.8", "3.9", "3.10"]
+        python: ["3.8", "3.9", "3.10", "3.11"]
         # this is to make the CI run on different sklearn versions
         include:
           - python: "3.8"
             sklearn_version: "1.0"
-          # TODO: add sklearn 1.1 when we add 3.11 support
           - python: "3.9"
-            sklearn_version: "1.2"
+            sklearn_version: "1.1"
           - python: "3.10"
+            sklearn_version: "1.2"
+          - python: "3.11"
             sklearn_version: "nightly"
 
 
diff --git a/setup.py b/setup.py
index 2262dcea..69d800a5 100644
--- a/setup.py
+++ b/setup.py
@@ -61,6 +61,7 @@ def setup_package():
             "Programming Language :: Python :: 3.8",
             "Programming Language :: Python :: 3.9",
             "Programming Language :: Python :: 3.10",
+            "Programming Language :: Python :: 3.11",
             "Programming Language :: Python :: Implementation :: CPython",
         ],
         python_requires=">=3.8",
diff --git a/skops/_min_dependencies.py b/skops/_min_dependencies.py
index 35219a12..565263fc 100644
--- a/skops/_min_dependencies.py
+++ b/skops/_min_dependencies.py
@@ -29,7 +29,8 @@
     # required for persistence tests of external libraries
     "lightgbm": ("3", "tests", None),
     "xgboost": ("1.6", "tests", None),
-    "catboost": ("1.0", "tests", None),
+    # TODO: remove condition when catboost supports python 3.11
+    "catboost": ("1.0", "tests", "python_version < '3.11'"),
 }
 
 
diff --git a/skops/io/_general.py b/skops/io/_general.py
index 10ef9a0f..9bc2254a 100644
--- a/skops/io/_general.py
+++ b/skops/io/_general.py
@@ -401,10 +401,11 @@ def _construct(self):
             return instance
 
         attrs = self.children["attrs"].construct()
-        if hasattr(instance, "__setstate__"):
-            instance.__setstate__(attrs)
-        else:
-            instance.__dict__.update(attrs)
+        if attrs is not None:
+            if hasattr(instance, "__setstate__"):
+                instance.__setstate__(attrs)
+            else:
+                instance.__dict__.update(attrs)
 
         return instance
 
diff --git a/skops/io/_sklearn.py b/skops/io/_sklearn.py
index 9da5392a..14ba4a87 100644
--- a/skops/io/_sklearn.py
+++ b/skops/io/_sklearn.py
@@ -72,13 +72,15 @@ def reduce_get_state(obj: Any, save_context: SaveContext) -> dict[str, Any]:
         # call __getstate__ directly.
         attrs = reduce[2]
     elif hasattr(obj, "__getstate__"):
-        attrs = obj.__getstate__()
+        # since python311 __getstate__ is defined for `object` and might return
+        # None
+        attrs = obj.__getstate__() or {}
     elif hasattr(obj, "__dict__"):
         attrs = obj.__dict__
     else:
         attrs = {}
 
-    if not isinstance(attrs, dict):
+    if not isinstance(attrs, (dict, tuple)):
         raise UnsupportedTypeException(
             f"Objects of type {res['__class__']} not supported yet"
         )
@@ -119,8 +121,13 @@ def _construct(self):
 
         if hasattr(instance, "__setstate__"):
             instance.__setstate__(attrs)
-        else:
+        elif isinstance(attrs, dict):
             instance.__dict__.update(attrs)
+        else:
+            # we (probably) got tuple attrs but cannot setstate with them
+            raise UnsupportedTypeException(
+                f"Objects of type {constructor} are not supported yet"
+            )
 
         return instance
 
diff --git a/skops/io/tests/_utils.py b/skops/io/tests/_utils.py
index 6b02c3af..9081a9fc 100644
--- a/skops/io/tests/_utils.py
+++ b/skops/io/tests/_utils.py
@@ -67,10 +67,13 @@ def _assert_tuples_equal(val1, val2):
 
 
 def _assert_vals_equal(val1, val2):
-    if hasattr(val1, "__getstate__"):
+    if type(val1) == type:  # e.g. could be np.int64
+        assert val1 is val2
+    elif hasattr(val1, "__getstate__") and (val1.__getstate__() is not None):
         # This includes BaseEstimator since they implement __getstate__ and
         # that returns the parameters as well.
-        #
+        # Since Python 3.11, all objects have a __getstate__ but they return
+        # None by default, in which case this check is not performed.
         # Some objects return a tuple of parameters, others a dict.
         state1 = val1.__getstate__()
         state2 = val2.__getstate__()
@@ -126,14 +129,9 @@ def _assert_vals_equal(val1, val2):
 
 
 def assert_params_equal(params1, params2):
-    # due to https://github.com/scikit-learn/scikit-learn/pull/22094, after
-    # loading an sklearn estimator, there might be an entry called
-    # "__sklearn_pickle_version__" in the __dict__ that wasn't there before. We
-    # just ignore it.
-    params1.pop("__sklearn_pickle_version__", None)
-    params2.pop("__sklearn_pickle_version__", None)
-
     # helper function to compare estimator dictionaries of parameters
+    if params1 is None and params2 is None:
+        return
     assert len(params1) == len(params2)
     assert set(params1.keys()) == set(params2.keys())
     for key in params1: