diff --git a/Library/Homebrew/cask/cask.rb b/Library/Homebrew/cask/cask.rb
index fd23cafada..89a7c19ad9 100644
--- a/Library/Homebrew/cask/cask.rb
+++ b/Library/Homebrew/cask/cask.rb
@@ -20,7 +20,7 @@ module Cask
 
     attr_reader :token, :sourcefile_path, :source, :config, :default_config
 
-    attr_accessor :download
+    attr_accessor :download, :allow_reassignment
 
     def self.all
       Tap.flat_map(&:cask_files).map do |f|
@@ -38,11 +38,12 @@ module Cask
       @tap
     end
 
-    def initialize(token, sourcefile_path: nil, source: nil, tap: nil, config: nil, &block)
+    def initialize(token, sourcefile_path: nil, source: nil, tap: nil, config: nil, allow_reassignment: false, &block)
       @token = token
       @sourcefile_path = sourcefile_path
       @source = source
       @tap = tap
+      @allow_reassignment = allow_reassignment
       @block = block
 
       @default_config = config || Config.new
diff --git a/Library/Homebrew/cask/dsl.rb b/Library/Homebrew/cask/dsl.rb
index e56bfc9a18..e4d1ac47a2 100644
--- a/Library/Homebrew/cask/dsl.rb
+++ b/Library/Homebrew/cask/dsl.rb
@@ -112,7 +112,7 @@ module Cask
     def set_unique_stanza(stanza, should_return)
       return instance_variable_get("@#{stanza}") if should_return
 
-      if instance_variable_defined?("@#{stanza}")
+      if !@cask.allow_reassignment && instance_variable_defined?("@#{stanza}")
         raise CaskInvalidError.new(cask, "'#{stanza}' stanza may only appear once.")
       end
 
@@ -137,7 +137,7 @@ module Cask
 
         return unless default
 
-        unless @language_blocks.default.nil?
+        if !@cask.allow_reassignment && @language_blocks.default.present?
           raise CaskInvalidError.new(cask, "Only one default language may be defined.")
         end
 
@@ -294,7 +294,9 @@ module Cask
       @livecheck ||= Livecheck.new(self)
       return @livecheck unless block
 
-      raise CaskInvalidError.new(cask, "'livecheck' stanza may only appear once.") if @livecheckable
+      if !@cask.allow_reassignment && @livecheckable
+        raise CaskInvalidError.new(cask, "'livecheck' stanza may only appear once.")
+      end
 
       @livecheckable = true
       @livecheck.instance_eval(&block)
diff --git a/Library/Homebrew/livecheck/livecheck.rb b/Library/Homebrew/livecheck/livecheck.rb
index f0a2056835..bdc25c3371 100644
--- a/Library/Homebrew/livecheck/livecheck.rb
+++ b/Library/Homebrew/livecheck/livecheck.rb
@@ -563,6 +563,7 @@ module Homebrew
 
     # Identifies the latest version of the formula and returns a Hash containing
     # the version information. Returns nil if a latest version couldn't be found.
+    # rubocop:disable Metrics/CyclomaticComplexity
     sig {
       params(
         formula_or_cask:            T.any(Formula, Cask::Cask),
@@ -657,7 +658,7 @@ module Homebrew
         end
 
         if livecheck_strategy.present?
-          if livecheck_url.blank?
+          if livecheck_url.blank? && strategy.method(:find_versions).parameters.include?([:keyreq, :url])
             odebug "#{strategy_name} strategy requires a URL"
             next
           elsif livecheck_strategy != :page_match && strategies.exclude?(strategy)
@@ -768,6 +769,7 @@ module Homebrew
 
       nil
     end
+    # rubocop:enable Metrics/CyclomaticComplexity
   end
   # rubocop:enable Metrics/ModuleLength
 end
diff --git a/Library/Homebrew/livecheck/strategy/extract_plist.rb b/Library/Homebrew/livecheck/strategy/extract_plist.rb
index 0bf114f63d..2486a545bc 100644
--- a/Library/Homebrew/livecheck/strategy/extract_plist.rb
+++ b/Library/Homebrew/livecheck/strategy/extract_plist.rb
@@ -82,25 +82,37 @@ module Homebrew
         # versions from `plist` files.
         #
         # @param cask [Cask::Cask] the cask to check for version information
+        # @param url [String, nil] an alternative URL to check for version
+        #   information
         # @param regex [Regexp, nil] a regex for use in a strategy block
         # @return [Hash]
         sig {
           params(
             cask:    Cask::Cask,
+            url:     T.nilable(String),
             regex:   T.nilable(Regexp),
             _unused: T.nilable(T::Hash[Symbol, T.untyped]),
             block:   T.untyped,
           ).returns(T::Hash[Symbol, T.untyped])
         }
-        def self.find_versions(cask:, regex: nil, **_unused, &block)
+        def self.find_versions(cask:, url: nil, regex: nil, **_unused, &block)
           if regex.present? && block.blank?
             raise ArgumentError, "#{T.must(name).demodulize} only supports a regex when using a `strategy` block"
           end
           raise ArgumentError, "The #{T.must(name).demodulize} strategy only supports casks." unless T.unsafe(cask)
 
-          match_data = { matches: {}, regex: regex }
+          match_data = { matches: {}, regex: regex, url: url }
+
+          unversioned_cask_checker = if url.present? && url != cask.url.to_s
+            # Create a copy of the `cask` that uses the `livecheck` block URL
+            cask_copy = Cask::CaskLoader.load(cask.full_name)
+            cask_copy.allow_reassignment = true
+            cask_copy.url { url }
+            UnversionedCaskChecker.new(cask_copy)
+          else
+            UnversionedCaskChecker.new(cask)
+          end
 
-          unversioned_cask_checker = UnversionedCaskChecker.new(cask)
           items = unversioned_cask_checker.all_versions.transform_values { |v| Item.new(bundle_version: v) }
 
           versions_from_items(items, regex, &block).each do |version_text|