diff --git a/Lib/test/libregrtest/tsan.py b/Lib/test/libregrtest/tsan.py
index 4fb0ee5038f3a9..df89b886d00bc0 100644
--- a/Lib/test/libregrtest/tsan.py
+++ b/Lib/test/libregrtest/tsan.py
@@ -37,6 +37,7 @@
 # the regression test runner with the `--parallel-threads` option enabled.
 TSAN_PARALLEL_TESTS = [
     'test_abc',
+    'test_exceptions',
     'test_hashlib',
 ]
 
diff --git a/Lib/test/support/__init__.py b/Lib/test/support/__init__.py
index 748b9b37117063..3b10d0ea534c10 100644
--- a/Lib/test/support/__init__.py
+++ b/Lib/test/support/__init__.py
@@ -2866,7 +2866,7 @@ def force_not_colorized(func):
     def wrapper(*args, **kwargs):
         with no_color():
             return func(*args, **kwargs)
-    return wrapper
+    return thread_unsafe(wrapper)  # modifying the environment is thread-unsafe
 
 
 def force_not_colorized_test_class(cls):
diff --git a/Lib/test/test_exceptions.py b/Lib/test/test_exceptions.py
index 20c617f8108d5f..d3c0087ce7c0e9 100644
--- a/Lib/test/test_exceptions.py
+++ b/Lib/test/test_exceptions.py
@@ -60,6 +60,7 @@ def raise_catch(self, exc, excname):
             self.assertEqual(buf1, buf2)
             self.assertEqual(exc.__name__, excname)
 
+    @support.thread_unsafe("TESTFN")
     def testRaising(self):
         self.raise_catch(AttributeError, "AttributeError")
         self.assertRaises(AttributeError, getattr, sys, "undefined_attribute")
@@ -1398,6 +1399,7 @@ def __str__(self):
             self.assertRaises(TypeError, str, exc)
 
     @no_tracing
+    @support.thread_unsafe("captures stderr")
     def test_badisinstance(self):
         # Bug #2542: if issubclass(e, MyException) raises an exception,
         # it should be ignored
@@ -1521,6 +1523,7 @@ def test_recursion_normalizing_infinite_exception(self):
         self.assertIn(b'Done.', out)
 
 
+    @support.thread_unsafe("uses sys.setrecursionlimit")
     def test_recursion_in_except_handler(self):
 
         def set_relative_recursion_limit(n):
@@ -1656,6 +1659,7 @@ class C(object):
 
     @cpython_only
     @unittest.skipIf(_testcapi is None, "requires _testcapi")
+    @support.thread_unsafe("gc_collect()")
     def test_memory_error_cleanup(self):
         # Issue #5437: preallocated MemoryError instances should not keep
         # traceback objects alive.
@@ -1705,6 +1709,7 @@ def test_errno_ENOTDIR(self):
             os.listdir(__file__)
         self.assertEqual(cm.exception.errno, errno.ENOTDIR, cm.exception)
 
+    @support.thread_unsafe("uses catch_unraisable_exception")
     def test_unraisable(self):
         # Issue #22836: PyErr_WriteUnraisable() should give sensible reports
         class BrokenDel:
@@ -1724,6 +1729,7 @@ def __del__(self):
                              f"deallocator {obj_repr}")
             self.assertIsNotNone(cm.unraisable.exc_traceback)
 
+    @support.thread_unsafe("captures stderr")
     def test_unhandled(self):
         # Check for sensible reporting of unhandled exceptions
         for exc_type in (ValueError, BrokenStrException):
@@ -1823,6 +1829,7 @@ def g():
                 next(i)
 
     @unittest.skipUnless(__debug__, "Won't work if __debug__ is False")
+    @support.thread_unsafe("modifies global AssertionError")
     def test_assert_shadowing(self):
         # Shadowing AssertionError would cause the assert statement to
         # misbehave.
@@ -1914,6 +1921,7 @@ def test_name_error_has_name(self):
         except NameError as exc:
             self.assertEqual("bluch", exc.name)
 
+    @support.thread_unsafe("captures stderr")
     def test_issue45826(self):
         # regression test for bpo-45826
         def f():
@@ -1930,6 +1938,7 @@ def f():
 
         self.assertIn("aab", err.getvalue())
 
+    @support.thread_unsafe("captures stderr")
     def test_issue45826_focused(self):
         def f():
             try:
@@ -2050,6 +2059,7 @@ def test_reset_attributes(self):
         self.assertEqual(exc.name, None)
         self.assertEqual(exc.path, None)
 
+    @support.thread_unsafe("check_warnings")
     def test_non_str_argument(self):
         # Issue #15778
         with check_warnings(('', BytesWarning), quiet=True):
@@ -2332,6 +2342,7 @@ class MySyntaxError(SyntaxError):
      ^^^^^
 """, err.getvalue())
 
+    @support.thread_unsafe("TESTFN")
     def test_encodings(self):
         self.addCleanup(unlink, TESTFN)
         source = (
diff --git a/Python/legacy_tracing.c b/Python/legacy_tracing.c
index dbd19d7755c237..28d803e6f999f9 100644
--- a/Python/legacy_tracing.c
+++ b/Python/legacy_tracing.c
@@ -528,6 +528,7 @@ _PyEval_SetProfile(PyThreadState *tstate, Py_tracefunc func, PyObject *arg)
 static Py_ssize_t
 setup_tracing(PyThreadState *tstate, Py_tracefunc func, PyObject *arg, PyObject **old_traceobj)
 {
+    assert(tstate->interp->sys_tracing_threads >= 0);
     *old_traceobj = NULL;
     /* Setup PEP 669 monitoring callbacks and events. */
     if (!tstate->interp->sys_trace_initialized) {
diff --git a/Tools/tsan/suppressions_free_threading.txt b/Tools/tsan/suppressions_free_threading.txt
index b0d64d36996920..81fb2eed1d38a5 100644
--- a/Tools/tsan/suppressions_free_threading.txt
+++ b/Tools/tsan/suppressions_free_threading.txt
@@ -32,6 +32,13 @@ race_top:mi_block_set_nextx
 # gh-127266: type slot updates are not thread-safe (test_opcache.test_load_attr_method_lazy_dict)
 race_top:update_one_slot
 
+# gh-129701: data race during modification of refcount when interning strings
+race:intern_common
+
+# gh-128130: race on _PyRuntime.signals.unhandled_keyboard_interrupt
+race_top:_PyErr_Display
+race_top:run_eval_code_obj
+
 # https://gist.github.com/mpage/6962e8870606cfc960e159b407a0cb40
 thread:pthread_create