diff --git a/pandas/core/frame.py b/pandas/core/frame.py
index 008c1e0d10ba4..847f514451add 100644
--- a/pandas/core/frame.py
+++ b/pandas/core/frame.py
@@ -4230,15 +4230,14 @@ def __setitem__(self, key, value) -> None:
                 warnings.warn(
                     _chained_assignment_msg, ChainedAssignmentError, stacklevel=2
                 )
-        # elif not PYPY and not using_copy_on_write():
-        elif not PYPY and warn_copy_on_write():
-            if sys.getrefcount(self) <= 3:  # and (
-                #     warn_copy_on_write()
-                #     or (
-                #         not warn_copy_on_write()
-                #         and self._mgr.blocks[0].refs.has_reference()
-                #     )
-                # ):
+        elif not PYPY and not using_copy_on_write():
+            if sys.getrefcount(self) <= 3 and (
+                warn_copy_on_write()
+                or (
+                    not warn_copy_on_write()
+                    and any(b.refs.has_reference() for b in self._mgr.blocks)  # type: ignore[union-attr]
+                )
+            ):
                 warnings.warn(
                     _chained_assignment_warning_msg, FutureWarning, stacklevel=2
                 )
diff --git a/pandas/tests/copy_view/test_chained_assignment_deprecation.py b/pandas/tests/copy_view/test_chained_assignment_deprecation.py
index 7b08d9b80fc9b..32d0f55f67185 100644
--- a/pandas/tests/copy_view/test_chained_assignment_deprecation.py
+++ b/pandas/tests/copy_view/test_chained_assignment_deprecation.py
@@ -1,9 +1,15 @@
 import numpy as np
 import pytest
 
-from pandas.errors import ChainedAssignmentError
+from pandas.errors import (
+    ChainedAssignmentError,
+    SettingWithCopyWarning,
+)
 
-from pandas import DataFrame
+from pandas import (
+    DataFrame,
+    option_context,
+)
 import pandas._testing as tm
 
 
@@ -85,3 +91,17 @@ def test_series_setitem(indexer, using_copy_on_write):
     else:
         assert record[0].category == FutureWarning
         assert "ChainedAssignmentError" in record[0].message.args[0]
+
+
+@pytest.mark.filterwarnings("ignore::pandas.errors.SettingWithCopyWarning")
+@pytest.mark.parametrize(
+    "indexer", ["a", ["a", "b"], slice(0, 2), np.array([True, False, True])]
+)
+def test_frame_setitem(indexer, using_copy_on_write):
+    df = DataFrame({"a": [1, 2, 3, 4, 5], "b": 1})
+
+    extra_warnings = () if using_copy_on_write else (SettingWithCopyWarning,)
+
+    with option_context("chained_assignment", "warn"):
+        with tm.raises_chained_assignment_error(extra_warnings=extra_warnings):
+            df[0:3][indexer] = 10
diff --git a/pandas/tests/indexing/multiindex/test_setitem.py b/pandas/tests/indexing/multiindex/test_setitem.py
index e613f1102b03b..53ad4d6b41687 100644
--- a/pandas/tests/indexing/multiindex/test_setitem.py
+++ b/pandas/tests/indexing/multiindex/test_setitem.py
@@ -548,7 +548,8 @@ def test_frame_setitem_copy_raises(
     else:
         msg = "A value is trying to be set on a copy of a slice from a DataFrame"
         with pytest.raises(SettingWithCopyError, match=msg):
-            df["foo"]["one"] = 2
+            with tm.raises_chained_assignment_error():
+                df["foo"]["one"] = 2
 
 
 def test_frame_setitem_copy_no_write(
@@ -563,7 +564,8 @@ def test_frame_setitem_copy_no_write(
     else:
         msg = "A value is trying to be set on a copy of a slice from a DataFrame"
         with pytest.raises(SettingWithCopyError, match=msg):
-            df["foo"]["one"] = 2
+            with tm.raises_chained_assignment_error():
+                df["foo"]["one"] = 2
 
     result = df
     tm.assert_frame_equal(result, expected)
diff --git a/pandas/tests/indexing/test_chaining_and_caching.py b/pandas/tests/indexing/test_chaining_and_caching.py
index 230c575e6ed10..88cac9b16f8f7 100644
--- a/pandas/tests/indexing/test_chaining_and_caching.py
+++ b/pandas/tests/indexing/test_chaining_and_caching.py
@@ -452,7 +452,8 @@ def test_detect_chained_assignment_undefined_column(
                 df.iloc[0:5]["group"] = "a"
         else:
             with pytest.raises(SettingWithCopyError, match=msg):
-                df.iloc[0:5]["group"] = "a"
+                with tm.raises_chained_assignment_error():
+                    df.iloc[0:5]["group"] = "a"
 
     @pytest.mark.arm_slow
     def test_detect_chained_assignment_changing_dtype(