Fix FP for invalid-name on module-level constant with multiple branches

Author: jacobtylerwalls

doc/whatsnew/fragments/10664.false_positive

@@ -0,0 +1,4 @@
+Fix a false positive for ``invalid-name`` on exclusive module-level assignments
+composed of three or more branches.
+
+Closes #10664

pylint/checkers/base/name_checker/checker.py

@@ -523,8 +523,11 @@ 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(

tests/functional/i/invalid/invalid_name/invalid_name_module_level.py

@@ -28,5 +28,7 @@ def A():  # [invalid-name]
 
 if CONST:
     OTHER_CONST = 1
-else:
+elif CONSTA:
     OTHER_CONST = 2
+else:
+    OTHER_CONST = 3