diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 2b679c5..5147f53 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -52,8 +52,13 @@ jobs:
     runs-on: ubuntu-latest
     strategy:
       matrix:
-        python-version: ['3.6', '3.7', '3.8', '3.9']
-        django-version: ['2.2', '3.0']
+        python-version: ['3.8', '3.9', '3.10']
+        django-version: ['3.2', '4.0']
+        include:
+          - python-version: '3.7'
+            django-version: '2.2'
+          - python-version: '3.6'
+            django-version: '2.2'
     steps:
       - uses: actions/checkout@v2
       - name: Setup system dependencies
diff --git a/django-stubs/core/servers/basehttp.pyi b/django-stubs/core/servers/basehttp.pyi
index 15a0cae..bef8ff8 100644
--- a/django-stubs/core/servers/basehttp.pyi
+++ b/django-stubs/core/servers/basehttp.pyi
@@ -20,7 +20,7 @@ class ServerHandler(simple_server.ServerHandler):
 
 class WSGIRequestHandler(simple_server.WSGIRequestHandler):
     close_connection: bool
-    connection: WSGIRequest
+    connection: WSGIRequest  # type: ignore[assignment]
     request: WSGIRequest
     rfile: BytesIO
     wfile: BytesIO
diff --git a/scripts/enabled_test_modules.py b/scripts/enabled_test_modules.py
index 3ff2cdb..a063fa2 100644
--- a/scripts/enabled_test_modules.py
+++ b/scripts/enabled_test_modules.py
@@ -111,6 +111,7 @@ IGNORED_ERRORS = {
         "Unsupported dynamic base class",
         'error: "HttpResponse" has no attribute "streaming_content"',
         'error: "HttpResponse" has no attribute "context_data"',
+        'Duplicate module named "apps"',
     ],
     "admin_checks": ['Argument 1 to "append" of "list" has incompatible type "str"; expected "CheckMessage"'],
     "admin_default_site": [
@@ -514,7 +515,7 @@ IGNORED_ERRORS = {
 
 
 def check_if_custom_ignores_are_covered_by_common() -> None:
-    from scripts.typecheck_tests import is_pattern_fits
+    from scripts.typecheck_tests import does_pattern_fit
 
     common_ignore_patterns = IGNORED_ERRORS["__common__"]
     for module_name, patterns in IGNORED_ERRORS.items():
@@ -522,7 +523,7 @@ def check_if_custom_ignores_are_covered_by_common() -> None:
             continue
         for pattern in patterns:
             for common_pattern in common_ignore_patterns:
-                if isinstance(pattern, str) and is_pattern_fits(common_pattern, pattern):
+                if isinstance(pattern, str) and does_pattern_fit(common_pattern, pattern):
                     print(f'pattern "{module_name}: {pattern!r}" is covered by pattern {common_pattern!r}')
 
 
diff --git a/scripts/typecheck_tests.py b/scripts/typecheck_tests.py
index dd4358f..f3ef999 100644
--- a/scripts/typecheck_tests.py
+++ b/scripts/typecheck_tests.py
@@ -11,9 +11,10 @@ from scripts.enabled_test_modules import EXTERNAL_MODULES, IGNORED_ERRORS, IGNOR
 from scripts.git_helpers import checkout_django_branch
 from scripts.paths import DJANGO_SOURCE_DIRECTORY, PROJECT_DIRECTORY
 
-DJANGO_COMMIT_REFS: Dict[str, str] = {
+DJANGO_COMMIT_REFS = {
     "2.2": "8093aaa8ff9dd7386a069c6eb49fcc1c5980c033",
-    "3.0": "44da7abda848f05caaed74f6a749038c87dedfda",
+    "3.2": "0153a63a674937e4a56d9d5e4ca2d629b011fbde",
+    "4.0": "67d0c4644acfd7707be4a31e8976f865509b09ac",
 }
 
 
@@ -28,7 +29,7 @@ def get_unused_ignores(ignored_message_freq: Dict[str, Dict[Union[str, Pattern],
     return unused_ignores
 
 
-def is_pattern_fits(pattern: Union[Pattern, str], line: str):
+def does_pattern_fit(pattern: Union[Pattern, str], line: str):
     if isinstance(pattern, Pattern):
         if pattern.search(line):
             return True
@@ -46,12 +47,12 @@ def is_ignored(line: str, test_folder_name: str, *, ignored_message_freqs: Dict[
         return True
 
     for pattern in IGNORED_ERRORS.get(test_folder_name, []):
-        if is_pattern_fits(pattern, line):
+        if does_pattern_fit(pattern, line):
             ignored_message_freqs[test_folder_name][pattern] += 1
             return True
 
     for pattern in IGNORED_ERRORS["__common__"]:
-        if is_pattern_fits(pattern, line):
+        if does_pattern_fit(pattern, line):
             ignored_message_freqs["__common__"][pattern] += 1
             return True