diff --git a/Library/Homebrew/cask/cask.rb b/Library/Homebrew/cask/cask.rb
index 475e0478fd6ce4..a939c4512a847a 100644
--- a/Library/Homebrew/cask/cask.rb
+++ b/Library/Homebrew/cask/cask.rb
@@ -117,7 +117,7 @@ def refresh
       @dsl.language_eval
     end
 
-    DSL::DSL_METHODS.each do |method_name|
+    ::Cask::DSL::DSL_METHODS.each do |method_name|
       define_method(method_name) { |&block| @dsl.send(method_name, &block) }
     end
 
diff --git a/Library/Homebrew/extend/on_system.rbi b/Library/Homebrew/extend/on_system.rbi
deleted file mode 100644
index 15534bb4b4dbca..00000000000000
--- a/Library/Homebrew/extend/on_system.rbi
+++ /dev/null
@@ -1,6 +0,0 @@
-# typed: strict
-
-module OnSystem::MacOSOnly
-  sig { params(arm: T.nilable(String), intel: T.nilable(String)).returns(T.nilable(String)) }
-  def on_arch_conditional(arm: nil, intel: nil); end
-end
diff --git a/Library/Homebrew/extend/os/mac/keg.rb b/Library/Homebrew/extend/os/mac/keg.rb
index aae4eb6ad35523..ec38822576fb60 100644
--- a/Library/Homebrew/extend/os/mac/keg.rb
+++ b/Library/Homebrew/extend/os/mac/keg.rb
@@ -3,6 +3,14 @@
 
 require "system_command"
 
+class Keg
+  GENERIC_MUST_BE_WRITABLE_DIRECTORIES = (remove_const :MUST_BE_WRITABLE_DIRECTORIES).freeze
+  MUST_BE_WRITABLE_DIRECTORIES = (
+    GENERIC_MUST_BE_WRITABLE_DIRECTORIES +
+    [HOMEBREW_PREFIX/"Frameworks"]
+  ).sort.uniq.freeze
+end
+
 module OS
   module Mac
     module Keg
diff --git a/Library/Homebrew/keg.rb b/Library/Homebrew/keg.rb
index 0b0f67d2564cdb..7d1a332a30290b 100644
--- a/Library/Homebrew/keg.rb
+++ b/Library/Homebrew/keg.rb
@@ -78,6 +78,32 @@ def to_s
   # Locale-specific directories have the form `language[_territory][.codeset][@modifier]`
   LOCALEDIR_RX = %r{(locale|man)/([a-z]{2}|C|POSIX)(_[A-Z]{2})?(\.[a-zA-Z\-0-9]+(@.+)?)?}
   INFOFILE_RX = %r{info/([^.].*?\.info(\.gz)?|dir)$}
+  KEG_LINK_DIRECTORIES = %w[
+    bin etc include lib sbin share var
+  ].freeze
+  MUST_EXIST_SUBDIRECTORIES = (
+    KEG_LINK_DIRECTORIES - %w[var] + %w[
+      opt
+      var/homebrew/linked
+    ]
+  ).map { |dir| HOMEBREW_PREFIX/dir }.sort.uniq.freeze
+  MUST_BE_WRITABLE_DIRECTORIES = (
+    %w[
+      etc/bash_completion.d lib/pkgconfig
+      share/aclocal share/doc share/info share/locale share/man
+      share/man/man1 share/man/man2 share/man/man3 share/man/man4
+      share/man/man5 share/man/man6 share/man/man7 share/man/man8
+      share/zsh share/zsh/site-functions
+      var/log
+    ].map { |dir| HOMEBREW_PREFIX/dir } + MUST_EXIST_SUBDIRECTORIES + [
+      HOMEBREW_CACHE,
+      HOMEBREW_CELLAR,
+      HOMEBREW_LOCKS,
+      HOMEBREW_LOGS,
+      HOMEBREW_REPOSITORY,
+      Language::Python.homebrew_site_packages,
+    ]
+  ).sort.uniq.freeze
 
   # These paths relative to the keg's share directory should always be real
   # directories in the prefix, never symlinks.