diff --git a/Library/Homebrew/rubocops/cask/no_overrides.rb b/Library/Homebrew/rubocops/cask/no_overrides.rb
index a5cfb8d9e1..4292a27b1b 100644
--- a/Library/Homebrew/rubocops/cask/no_overrides.rb
+++ b/Library/Homebrew/rubocops/cask/no_overrides.rb
@@ -41,9 +41,7 @@ module RuboCop
             node.child_nodes.each do |child|
               child.each_node(:send) do |send_node|
                 # Skip (nested) livecheck blocks as its `url` is different to a download `url`.
-                next if send_node.method_name == :livecheck
-                next if send_node.parent.block_type? && send_node.parent.method_name == :livecheck
-
+                next if send_node.method_name == :livecheck || inside_livecheck_block?(send_node)
                 # Skip string interpolations (`:send` inside `:begin` inside `:dstr`).
                 next if send_node.parent.begin_type? && send_node.parent.parent.dstr_type?
                 next if ON_SYSTEM_METHODS.include?(send_node.method_name)
@@ -54,6 +52,19 @@ module RuboCop
           end
           names
         end
+
+        def inside_livecheck_block?(node)
+          single_stanza_livecheck_block?(node) || multi_stanza_livecheck_block?(node)
+        end
+
+        def single_stanza_livecheck_block?(node)
+          node.parent.block_type? && node.parent.method_name == :livecheck
+        end
+
+        def multi_stanza_livecheck_block?(node)
+          grandparent_node = node.parent.parent
+          node.parent.begin_type? && grandparent_node.block_type? && grandparent_node.method_name == :livecheck
+        end
       end
     end
   end
diff --git a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
index 9cee740498..a552a31d66 100644
--- a/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
+++ b/Library/Homebrew/test/rubocops/cask/no_overrides_spec.rb
@@ -46,6 +46,7 @@ describe RuboCop::Cop::Cask::NoOverrides do
           version '1.2.3'
           on_mojave :or_later do
             url "https://brew.sh/foo-\#{version}-\#{arch}.pkg"
+            sha256 "aaa"
           end
         end
       CASK
@@ -54,7 +55,30 @@ describe RuboCop::Cop::Cask::NoOverrides do
     include_examples "does not report any offenses"
   end
 
-  context "when there are livecheck blocks within `on_*` blocks, ignore their contents" do
+  context "when there are single-line livecheck blocks within `on_*` blocks, ignore their contents" do
+    let(:source) do
+      <<~CASK
+        cask 'foo' do
+          on_intel do
+            livecheck do
+              url 'https://brew.sh/foo' # Livecheck should be allowed since it's a different "kind" of URL.
+            end
+            version '1.2.3'
+          end
+          on_arm do
+            version '2.3.4'
+          end
+
+          url 'https://brew.sh/foo.pkg'
+          sha256 "bbb"
+        end
+      CASK
+    end
+
+    include_examples "does not report any offenses"
+  end
+
+  context "when there are multi-line livecheck blocks within `on_*` blocks, ignore their contents" do
     let(:source) do
       <<~CASK
         cask 'foo' do
@@ -70,6 +94,7 @@ describe RuboCop::Cop::Cask::NoOverrides do
           end
 
           url 'https://brew.sh/foo.pkg'
+          sha256 "bbb"
         end
       CASK
     end