diff --git a/pandas/tests/extension/base/accumulate.py b/pandas/tests/extension/base/accumulate.py
index 6774fcc27f35c..d60b41ccbb46e 100644
--- a/pandas/tests/extension/base/accumulate.py
+++ b/pandas/tests/extension/base/accumulate.py
@@ -11,28 +11,32 @@ class BaseAccumulateTests(BaseExtensionTests):
     make sense for numeric/boolean operations.
     """
 
-    def check_accumulate(self, s, op_name, skipna):
-        result = getattr(s, op_name)(skipna=skipna)
+    def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
+        # Do we expect this accumulation to be supported for this dtype?
+        # We default to assuming "no"; subclass authors should override here.
+        return False
+
+    def check_accumulate(self, ser: pd.Series, op_name: str, skipna: bool):
+        alt = ser.astype("float64")
+        result = getattr(ser, op_name)(skipna=skipna)
 
         if result.dtype == pd.Float32Dtype() and op_name == "cumprod" and skipna:
+            # TODO: avoid special-casing here
             pytest.skip(
                 f"Float32 precision lead to large differences with op {op_name} "
                 f"and skipna={skipna}"
             )
 
-        expected = getattr(s.astype("float64"), op_name)(skipna=skipna)
+        expected = getattr(alt, op_name)(skipna=skipna)
         tm.assert_series_equal(result, expected, check_dtype=False)
 
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series_raises(self, data, all_numeric_accumulations, skipna):
-        op_name = all_numeric_accumulations
-        ser = pd.Series(data)
-
-        with pytest.raises(NotImplementedError):
-            getattr(ser, op_name)(skipna=skipna)
-
     @pytest.mark.parametrize("skipna", [True, False])
     def test_accumulate_series(self, data, all_numeric_accumulations, skipna):
         op_name = all_numeric_accumulations
         ser = pd.Series(data)
-        self.check_accumulate(ser, op_name, skipna)
+
+        if self._supports_accumulation(ser, op_name):
+            self.check_accumulate(ser, op_name, skipna)
+        else:
+            with pytest.raises(NotImplementedError):
+                getattr(ser, op_name)(skipna=skipna)
diff --git a/pandas/tests/extension/test_arrow.py b/pandas/tests/extension/test_arrow.py
index 29fcd4e48db46..bd5a9d8405b13 100644
--- a/pandas/tests/extension/test_arrow.py
+++ b/pandas/tests/extension/test_arrow.py
@@ -354,47 +354,30 @@ def check_accumulate(self, ser, op_name, skipna):
         expected = getattr(ser.astype("Float64"), op_name)(skipna=skipna)
         tm.assert_series_equal(result, expected, check_dtype=False)
 
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series_raises(self, data, all_numeric_accumulations, skipna):
-        pa_type = data.dtype.pyarrow_dtype
-        if (
-            (
-                pa.types.is_integer(pa_type)
-                or pa.types.is_floating(pa_type)
-                or pa.types.is_duration(pa_type)
-            )
-            and all_numeric_accumulations == "cumsum"
-            and not pa_version_under9p0
-        ):
-            pytest.skip("These work, are tested by test_accumulate_series.")
+    def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
+        pa_type = ser.dtype.pyarrow_dtype
 
-        op_name = all_numeric_accumulations
-        ser = pd.Series(data)
-
-        with pytest.raises(NotImplementedError):
-            getattr(ser, op_name)(skipna=skipna)
-
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series(self, data, all_numeric_accumulations, skipna, request):
-        pa_type = data.dtype.pyarrow_dtype
-        op_name = all_numeric_accumulations
-        ser = pd.Series(data)
-
-        do_skip = False
         if pa.types.is_string(pa_type) or pa.types.is_binary(pa_type):
             if op_name in ["cumsum", "cumprod"]:
-                do_skip = True
+                return False
         elif pa.types.is_temporal(pa_type) and not pa.types.is_duration(pa_type):
             if op_name in ["cumsum", "cumprod"]:
-                do_skip = True
+                return False
         elif pa.types.is_duration(pa_type):
             if op_name == "cumprod":
-                do_skip = True
+                return False
+        return True
 
-        if do_skip:
-            pytest.skip(
-                f"{op_name} should *not* work, we test in "
-                "test_accumulate_series_raises that these correctly raise."
+    @pytest.mark.parametrize("skipna", [True, False])
+    def test_accumulate_series(self, data, all_numeric_accumulations, skipna, request):
+        pa_type = data.dtype.pyarrow_dtype
+        op_name = all_numeric_accumulations
+        ser = pd.Series(data)
+
+        if not self._supports_accumulation(ser, op_name):
+            # The base class test will check that we raise
+            return super().test_accumulate_series(
+                data, all_numeric_accumulations, skipna
             )
 
         if all_numeric_accumulations != "cumsum" or pa_version_under9p0:
diff --git a/pandas/tests/extension/test_boolean.py b/pandas/tests/extension/test_boolean.py
index 24095f807d4ae..97b0e814c526d 100644
--- a/pandas/tests/extension/test_boolean.py
+++ b/pandas/tests/extension/test_boolean.py
@@ -272,6 +272,9 @@ class TestUnaryOps(base.BaseUnaryOpsTests):
 
 
 class TestAccumulation(base.BaseAccumulateTests):
+    def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
+        return True
+
     def check_accumulate(self, s, op_name, skipna):
         length = 64
         if not IS64 or is_platform_windows():
@@ -286,10 +289,6 @@ def check_accumulate(self, s, op_name, skipna):
             expected = expected.astype("boolean")
         tm.assert_series_equal(result, expected)
 
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series_raises(self, data, all_numeric_accumulations, skipna):
-        pass
-
 
 class TestParsing(base.BaseParsingTests):
     pass
diff --git a/pandas/tests/extension/test_categorical.py b/pandas/tests/extension/test_categorical.py
index a712e2992c120..fc4dfe3af3bca 100644
--- a/pandas/tests/extension/test_categorical.py
+++ b/pandas/tests/extension/test_categorical.py
@@ -157,9 +157,7 @@ class TestReduce(base.BaseNoReduceTests):
 
 
 class TestAccumulate(base.BaseAccumulateTests):
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series(self, data, all_numeric_accumulations, skipna):
-        pass
+    pass
 
 
 class TestMethods(base.BaseMethodsTests):
diff --git a/pandas/tests/extension/test_masked_numeric.py b/pandas/tests/extension/test_masked_numeric.py
index 321321e0760d5..6ae9cdecc101a 100644
--- a/pandas/tests/extension/test_masked_numeric.py
+++ b/pandas/tests/extension/test_masked_numeric.py
@@ -324,9 +324,8 @@ class TestBooleanReduce(base.BaseBooleanReduceTests):
 
 
 class TestAccumulation(base.BaseAccumulateTests):
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series_raises(self, data, all_numeric_accumulations, skipna):
-        pass
+    def _supports_accumulation(self, ser: pd.Series, op_name: str) -> bool:
+        return True
 
     def check_accumulate(self, ser: pd.Series, op_name: str, skipna: bool):
         # overwrite to ensure pd.NA is tested instead of np.nan
diff --git a/pandas/tests/extension/test_sparse.py b/pandas/tests/extension/test_sparse.py
index 748d5cc65de1a..d8b04b41a8c6b 100644
--- a/pandas/tests/extension/test_sparse.py
+++ b/pandas/tests/extension/test_sparse.py
@@ -475,6 +475,4 @@ def test_EA_types(self, engine, data):
 
 
 class TestNoNumericAccumulations(base.BaseAccumulateTests):
-    @pytest.mark.parametrize("skipna", [True, False])
-    def test_accumulate_series(self, data, all_numeric_accumulations, skipna):
-        pass
+    pass