diff --git a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
index 4cbfc9d765..cd1dc3c436 100644
--- a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
+++ b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
@@ -59,6 +59,47 @@ describe RuboCop::Cop::Cask::NoOverrides do
     include_examples "does not report any offenses"
   end
 
+  context "when there are multiple differences between the `on_*` blocks" do
+    let(:source) do
+      <<~CASK
+        cask "foo" do
+          version "1.2.3"
+          sha256 "aaa"
+          url "https://brew.sh/foo-2.3.4.dmg"
+
+          on_big_sur :or_older do
+            sha256 "bbb"
+            url "https://brew.sh/legacy/foo-2.3.4.dmg"
+          end
+        end
+      CASK
+    end
+
+    let(:expected_offenses) do
+      [{
+        message:  <<~EOS,
+          Do not use a top-level `sha256` stanza as the default. Add it to an `on_{system}` block instead.
+          Use `:or_older` or `:or_newer` to specify a range of macOS versions.
+        EOS
+        severity: :convention,
+        line:     3,
+        column:   2,
+        source:   "sha256 \"aaa\"",
+      }, {
+        message:  <<~EOS,
+          Do not use a top-level `url` stanza as the default. Add it to an `on_{system}` block instead.
+          Use `:or_older` or `:or_newer` to specify a range of macOS versions.
+        EOS
+        severity: :convention,
+        line:     4,
+        column:   2,
+        source:   "url \"https://brew.sh/foo-2.3.4.dmg\"",
+      }]
+    end
+
+    include_examples "reports offenses"
+  end
+
   context "when there are top-level standalone stanzas" do
     let(:source) do
       <<~CASK