diff --git a/Library/Homebrew/cask/artifact/uninstall.rb b/Library/Homebrew/cask/artifact/uninstall.rb
index a91efd2fa8..4b83e18325 100644
--- a/Library/Homebrew/cask/artifact/uninstall.rb
+++ b/Library/Homebrew/cask/artifact/uninstall.rb
@@ -3,17 +3,26 @@
 
 require "cask/artifact/abstract_uninstall"
 
+UPGRADE_REINSTALL_SKIP_DIRECTIVES = [:quit, :signal].freeze
+
 module Cask
   module Artifact
     # Artifact corresponding to the `uninstall` stanza.
     #
     # @api private
     class Uninstall < AbstractUninstall
-      def uninstall_phase(**options)
-        ORDERED_DIRECTIVES.reject { |directive_sym| directive_sym == :rmdir }
-                          .each do |directive_sym|
-                            dispatch_uninstall_directive(directive_sym, **options)
-                          end
+      def uninstall_phase(upgrade: false, reinstall: false, **options)
+        filtered_directives = ORDERED_DIRECTIVES.filter do |directive_sym|
+          next false if directive_sym == :rmdir
+
+          next false if (upgrade || reinstall) && UPGRADE_REINSTALL_SKIP_DIRECTIVES.include?(directive_sym)
+
+          true
+        end
+
+        filtered_directives.each do |directive_sym|
+          dispatch_uninstall_directive(directive_sym, **options)
+        end
       end
 
       def post_uninstall_phase(**options)
diff --git a/Library/Homebrew/cask/installer.rb b/Library/Homebrew/cask/installer.rb
index 0cacc005fd..cb9d11930f 100644
--- a/Library/Homebrew/cask/installer.rb
+++ b/Library/Homebrew/cask/installer.rb
@@ -472,6 +472,8 @@ on_request: true)
             skip:      clear,
             force:     force?,
             successor: successor,
+            upgrade:   upgrade?,
+            reinstall: reinstall?,
           )
         end
 
diff --git a/Library/Homebrew/test/cask/artifact/shared_examples/uninstall_zap.rb b/Library/Homebrew/test/cask/artifact/shared_examples/uninstall_zap.rb
index ec195718f0..872a154ae5 100644
--- a/Library/Homebrew/test/cask/artifact/shared_examples/uninstall_zap.rb
+++ b/Library/Homebrew/test/cask/artifact/shared_examples/uninstall_zap.rb
@@ -228,6 +228,20 @@ shared_examples "#uninstall_phase or #zap_phase" do
       end.to output(/Application 'my.fancy.package.app' quit successfully\./).to_stdout
     end
 
+    it "does not attempt to quit when upgrading or reinstalling" do
+      next if artifact_dsl_key == :zap
+
+      allow(User.current).to receive(:gui?).and_return true
+
+      expect(subject).not_to receive(:running?)
+      expect(subject).not_to receive(:quit)
+
+      expect do
+        subject.public_send(:"#{artifact_dsl_key}_phase", upgrade: true, command: fake_system_command)
+        subject.public_send(:"#{artifact_dsl_key}_phase", reinstall: true, command: fake_system_command)
+      end
+    end
+
     it "tries to quit the application for 10 seconds" do
       allow(User.current).to receive(:gui?).and_return true
 
@@ -261,6 +275,20 @@ shared_examples "#uninstall_phase or #zap_phase" do
 
       subject.public_send(:"#{artifact_dsl_key}_phase", command: fake_system_command)
     end
+
+    it "does not send signal when upgrading or reinstalling" do
+      next if artifact_dsl_key == :zap
+
+      allow(subject).to receive(:running_processes).with(bundle_id)
+                                                   .and_return(unix_pids.map { |pid| [pid, 0, bundle_id] })
+
+      signals.each do |_signal|
+        expect(Process).not_to receive(:kill)
+      end
+
+      subject.public_send(:"#{artifact_dsl_key}_phase", upgrade: true, command: fake_system_command)
+      subject.public_send(:"#{artifact_dsl_key}_phase", reinstall: true, command: fake_system_command)
+    end
   end
 
   [:delete, :trash].each do |directive|
diff --git a/docs/Cask-Cookbook.md b/docs/Cask-Cookbook.md
index 49aee219b9..6b9d230528 100644
--- a/docs/Cask-Cookbook.md
+++ b/docs/Cask-Cookbook.md
@@ -761,8 +761,8 @@ Since `pkg` installers can do arbitrary things, different techniques are needed
 
 * **`early_script:`** (string or hash) - like [`script:`](#uninstall-script), but runs early (for special cases, best avoided)
 * [`launchctl:`](#uninstall-launchctl) (string or array) - IDs of `launchd` jobs to remove
-* [`quit:`](#uninstall-quit) (string or array) - bundle IDs of running applications to quit
-* [`signal:`](#uninstall-signal) (array of arrays) - signal numbers and bundle IDs of running applications to send a Unix signal to (for when `quit:` does not work)
+* [`quit:`](#uninstall-quit) (string or array) - bundle IDs of running applications to quit (does not run when uninstall is initiated by `brew upgrade` or `brew reinstall`)
+* [`signal:`](#uninstall-signal) (array of arrays) - signal numbers and bundle IDs of running applications to send a Unix signal to - for when `quit:` does not work (does not run when uninstall is initiated by `brew upgrade` or `brew reinstall`)
 * [`login_item:`](#uninstall-login_item) (string or array) - names of login items to remove
 * [`kext:`](#uninstall-kext) (string or array) - bundle IDs of kexts to unload from the system
 * [`script:`](#uninstall-script) (string or hash) - relative path to an uninstall script to be run via sudo; use hash if args are needed