diff --git a/Library/Homebrew/rubocops/cask/ast/cask_block.rb b/Library/Homebrew/rubocops/cask/ast/cask_block.rb
index c05f109723..4f45f6771c 100644
--- a/Library/Homebrew/rubocops/cask/ast/cask_block.rb
+++ b/Library/Homebrew/rubocops/cask/ast/cask_block.rb
@@ -49,7 +49,7 @@ module RuboCop
           stanzas.sort do |s1, s2|
             i1 = stanza_order_index(s1)
             i2 = stanza_order_index(s2)
-            if i1 == i2
+            if i1 == i2 || i1.blank? || i2.blank?
               i1 = stanzas.index(s1)
               i2 = stanzas.index(s2)
             end
diff --git a/Library/Homebrew/rubocops/cask/constants/stanza.rb b/Library/Homebrew/rubocops/cask/constants/stanza.rb
index 5294a1c45f..d8129cc51b 100644
--- a/Library/Homebrew/rubocops/cask/constants/stanza.rb
+++ b/Library/Homebrew/rubocops/cask/constants/stanza.rb
@@ -55,6 +55,8 @@ module RuboCop
         end.freeze
 
       STANZA_ORDER = STANZA_GROUPS.flatten.freeze
+
+      ON_SYSTEM_METHODS = [:arm, :intel, *MacOSVersions::SYMBOLS.keys].map { |option| :"on_#{option}" }.freeze
     end
   end
 end
diff --git a/Library/Homebrew/rubocops/cask/extend/node.rb b/Library/Homebrew/rubocops/cask/extend/node.rb
index c0c4f5f993..50e93a5743 100644
--- a/Library/Homebrew/rubocops/cask/extend/node.rb
+++ b/Library/Homebrew/rubocops/cask/extend/node.rb
@@ -19,8 +19,10 @@ module RuboCop
 
       def stanza?
         return true if arch_variable?
+        return false if !send_type? && !block_type?
+        return true if ON_SYSTEM_METHODS.include?(method_name)
 
-        (send_type? || block_type?) && STANZA_ORDER.include?(method_name)
+        STANZA_ORDER.include?(method_name)
       end
 
       def heredoc?
diff --git a/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb b/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
index 05a29fd20f..02a9e28fc1 100644
--- a/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
+++ b/Library/Homebrew/test/support/fixtures/cask/Casks/multiple-versions.rb
@@ -9,7 +9,6 @@ cask "multiple-versions" do
     version "1.2.0"
     sha256 "8c62a2b791cf5f0da6066a0a4b6e85f62949cd60975da062df44adf887f4370b"
   end
-
   on_catalina :or_older do
     version "1.0.0"
     sha256 "1866dfa833b123bb8fe7fa7185ebf24d28d300d0643d75798bc23730af734216"