diff --git a/scrapy/downloadermiddlewares/cookies.py b/scrapy/downloadermiddlewares/cookies.py
index 6495157d765..b2227dd8d8b 100644
--- a/scrapy/downloadermiddlewares/cookies.py
+++ b/scrapy/downloadermiddlewares/cookies.py
@@ -43,10 +43,11 @@ def _process_cookies(self, cookies, *, jar, request):
 
             if cookie_domain and _is_public_domain(cookie_domain):
                 if cookie_domain != request_domain:
-                    continue
-                cookie.domain = request_domain
-
-            jar.set_cookie_if_ok(cookie, request)
+                    cookie.domain = request_domain
+                jar.set_cookie_if_ok(cookie, request)
+            else:
+                print(f'seting cookie {cookie.__dict__}')
+                jar.set_cookie(cookie)
 
     def process_request(self, request, spider):
         if request.meta.get("dont_merge_cookies", False):
diff --git a/tests/test_downloadermiddleware_cookies.py b/tests/test_downloadermiddleware_cookies.py
index 4a81a638ee1..af43e4bc3d7 100644
--- a/tests/test_downloadermiddleware_cookies.py
+++ b/tests/test_downloadermiddleware_cookies.py
@@ -646,7 +646,7 @@ def test_user_set_cookie_domain_suffix_public_period(self):
             "https://foo.co.uk",
             "https://bar.co.uk",
             "co.uk",
-            cookies1=False,
+            cookies1=True,
             cookies2=False,
         )
 
@@ -655,7 +655,7 @@ def test_user_set_cookie_domain_suffix_public_private(self):
             "https://foo.blogspot.com",
             "https://bar.blogspot.com",
             "blogspot.com",
-            cookies1=False,
+            cookies1=True,
             cookies2=False,
         )
 
@@ -732,3 +732,23 @@ def test_server_set_cookie_domain_public_period(self):
             "co.uk",
             cookies=True,
         )
+
+    def test_off_domain_jar_storage(self):
+        request1 = Request(
+            "https://a.example",
+            cookies=[
+                {
+                    "name": "foo",
+                    "value": "bar",
+                    "domain": "b.example",
+                },
+            ],
+        )
+        print(f'processing request1 {request1}')
+        assert self.mw.process_request(request1, self.spider) is None
+        self.assertNotIn(b"Cookie", request1.headers)
+
+        request2 = Request("https://b.example/")
+        print(f'processing request2 {request2}')
+        assert self.mw.process_request(request2, self.spider) is None
+        self.assertEqual(request2.headers.get(b"Cookie"), b"foo=bar")