diff --git a/doc/whatsnew/fragments/10664.false_positive b/doc/whatsnew/fragments/10664.false_positive
new file mode 100644
index 0000000000..3e0716ac50
--- /dev/null
+++ b/doc/whatsnew/fragments/10664.false_positive
@@ -0,0 +1,5 @@
+Fix a false positive for ``invalid-name`` on exclusive module-level assignments
+composed of three or more branches. We won't raise ``disallowed-name`` on module-level names that can't be inferred
+until a further refactor to remove this false negative is done.
+
+Closes #10664
diff --git a/pylint/checkers/base/name_checker/checker.py b/pylint/checkers/base/name_checker/checker.py
index 29fb52d051..c2f2655282 100644
--- a/pylint/checkers/base/name_checker/checker.py
+++ b/pylint/checkers/base/name_checker/checker.py
@@ -523,16 +523,22 @@ def visit_assignname(  # pylint: disable=too-many-branches,too-many-statements
                     if (
                         (iattrs := tuple(node.frame().igetattr(node.name)))
                         and util.Uninferable not in iattrs
-                        and len(iattrs) == 2
-                        and astroid.are_exclusive(*iattrs)
+                        and len(iattrs) > 1
+                        and all(
+                            astroid.are_exclusive(*combo)
+                            for combo in itertools.combinations(iattrs, 2)
+                        )
                     ):
                         node_type = "const"
-                    self._check_name(
-                        node_type,
-                        node.name,
-                        node,
-                        disallowed_check_only=redefines_import,
-                    )
+                    if not self._meets_exception_for_non_consts(
+                        inferred_assign_type, node.name
+                    ):
+                        self._check_name(
+                            node_type,
+                            node.name,
+                            node,
+                            disallowed_check_only=redefines_import,
+                        )
 
         # Check names defined in function scopes
         elif isinstance(frame, nodes.FunctionDef):
diff --git a/tests/functional/d/disallowed_name.py b/tests/functional/d/disallowed_name.py
index a6155dd346..21ffffcc5c 100644
--- a/tests/functional/d/disallowed_name.py
+++ b/tests/functional/d/disallowed_name.py
@@ -6,6 +6,6 @@ def baz():  # [disallowed-name]
 class foo():  # [disallowed-name]
     pass
 
-foo = {}.keys()  # [disallowed-name]
+foo = {}.keys()  # Should raise disallowed-name once _check_name() is refactored.
 foo = 42  # [disallowed-name]
 aaa = 42  # [invalid-name]
diff --git a/tests/functional/d/disallowed_name.txt b/tests/functional/d/disallowed_name.txt
index 535510a532..728d58aa6d 100644
--- a/tests/functional/d/disallowed_name.txt
+++ b/tests/functional/d/disallowed_name.txt
@@ -1,5 +1,4 @@
 disallowed-name:3:0:3:7:baz:"Disallowed name ""baz""":HIGH
 disallowed-name:6:0:6:9:foo:"Disallowed name ""foo""":HIGH
-disallowed-name:9:0:9:3::"Disallowed name ""foo""":HIGH
 disallowed-name:10:0:10:3::"Disallowed name ""foo""":HIGH
 invalid-name:11:0:11:3::"Constant name ""aaa"" doesn't conform to UPPER_CASE naming style":HIGH
diff --git a/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py b/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
index 8c2c2f2482..9012cea417 100644
--- a/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
+++ b/tests/functional/i/invalid/invalid_name/invalid_name_module_level.py
@@ -26,7 +26,19 @@ def A():  # [invalid-name]
 ASSIGNMENT_THAT_CRASHED_PYLINT = type(float.__new__.__code__)
 
 
+# Exclusive assignment: uses const regex
 if CONST:
     OTHER_CONST = 1
-else:
+elif CONSTA:
     OTHER_CONST = 2
+else:
+    OTHER_CONST = 3
+
+
+# Lists, sets, and objects can pass against the variable OR const regexes.
+if CONST:
+    other_const = [1]
+elif CONSTA:
+    other_const = [2]
+else:
+    other_const = [3]