diff --git a/Library/Homebrew/cli/args.rbi b/Library/Homebrew/cli/args.rbi
index 004dc2fb2..a40455d22 100644
--- a/Library/Homebrew/cli/args.rbi
+++ b/Library/Homebrew/cli/args.rbi
@@ -293,6 +293,9 @@ module Homebrew
 
       sig { returns(T::Boolean) }
       def write_only?; end
+
+      sig { returns(T::Boolean) }
+      def custom_remote?; end
     end
   end
 end
diff --git a/Library/Homebrew/cmd/tap.rb b/Library/Homebrew/cmd/tap.rb
index f044c18df..c81b369aa 100644
--- a/Library/Homebrew/cmd/tap.rb
+++ b/Library/Homebrew/cmd/tap.rb
@@ -35,6 +35,8 @@ module Homebrew
       switch "--force-auto-update",
              description: "Auto-update tap even if it is not hosted on GitHub. By default, only taps "\
                           "hosted on GitHub are auto-updated (for performance reasons)."
+      switch "--custom-remote",
+             description: "Install or change a tap with a custom remote. Useful for mirrors."
       switch "--repair",
              description: "Migrate tapped formulae from symlink-based to directory-based structure."
       switch "--list-pinned",
@@ -64,8 +66,9 @@ module Homebrew
       begin
         tap.install clone_target:      args.named.second,
                     force_auto_update: force_auto_update?(args: args),
+                    custom_remote:     args.custom_remote?,
                     quiet:             args.quiet?
-      rescue TapRemoteMismatchError => e
+      rescue TapRemoteMismatchError, TapNoCustomRemoteError => e
         odie e
       rescue TapAlreadyTappedError
         nil
diff --git a/Library/Homebrew/exceptions.rb b/Library/Homebrew/exceptions.rb
index 02928cf3f..58aa822dc 100644
--- a/Library/Homebrew/exceptions.rb
+++ b/Library/Homebrew/exceptions.rb
@@ -324,13 +324,28 @@ class TapRemoteMismatchError < RuntimeError
     @expected_remote = expected_remote
     @actual_remote = actual_remote
 
-    super <<~EOS
+    super message
+  end
+
+  def message
+    <<~EOS
       Tap #{name} remote mismatch.
       #{expected_remote} != #{actual_remote}
     EOS
   end
 end
 
+# Raised when the remote of Homebrew/core does not match HOMEBREW_CORE_GIT_REMOTE.
+class TapCoreRemoteMismatchError < TapRemoteMismatchError
+  def message
+    <<~EOS
+      Tap #{name} remote does mot match HOMEBREW_CORE_GIT_REMOTE.
+      #{expected_remote} != #{actual_remote}
+      Please set HOMEBREW_CORE_GIT_REMOTE="#{actual_remote}" and run `brew update` instead.
+    EOS
+  end
+end
+
 # Raised when a tap is already installed.
 class TapAlreadyTappedError < RuntimeError
   attr_reader :name
@@ -344,6 +359,19 @@ class TapAlreadyTappedError < RuntimeError
   end
 end
 
+# Raised when run `brew tap --custom-remote` without a remote URL.
+class TapNoCustomRemoteError < RuntimeError
+  attr_reader :name
+
+  def initialize(name)
+    @name = name
+
+    super <<~EOS
+      Tap #{name} with option `--custom-remote` but without a remote URL.
+    EOS
+  end
+end
+
 # Raised when another Homebrew operation is already in progress.
 class OperationInProgressError < RuntimeError
   def initialize(name)
diff --git a/Library/Homebrew/tap.rb b/Library/Homebrew/tap.rb
index 23b61b2c9..8d8a792c4 100644
--- a/Library/Homebrew/tap.rb
+++ b/Library/Homebrew/tap.rb
@@ -246,7 +246,8 @@ class Tap
   # @param force_auto_update [Boolean, nil] If present, whether to override the
   #   logic that skips non-GitHub repositories during auto-updates.
   # @param quiet [Boolean] If set, suppress all output.
-  def install(quiet: false, clone_target: nil, force_auto_update: nil)
+  # @param custom_remote [Boolean] If set, change the tap's remote if already installed.
+  def install(quiet: false, clone_target: nil, force_auto_update: nil, custom_remote: false)
     require "descriptions"
     require "readall"
 
@@ -257,9 +258,11 @@ class Tap
       odie "#{name} was moved. Tap homebrew/#{new_repo} instead."
     end
 
+    raise TapNoCustomRemoteError, name if custom_remote && clone_target.nil?
+
     requested_remote = clone_target || default_remote
 
-    if installed?
+    if installed? && !custom_remote
       raise TapRemoteMismatchError.new(name, @remote, requested_remote) if clone_target && requested_remote != remote
       raise TapAlreadyTappedError, name if force_auto_update.nil? && !shallow?
     end
@@ -268,6 +271,10 @@ class Tap
     Utils::Git.ensure_installed!
 
     if installed?
+      if requested_remote != remote # we are sure that clone_target is not nil and custom_remote is true here
+        fix_remote_configuration(requested_remote: requested_remote, quiet: quiet)
+      end
+
       unless force_auto_update.nil?
         config["forceautoupdate"] = force_auto_update
         return
@@ -358,20 +365,33 @@ class Tap
     end
   end
 
-  def fix_remote_configuration
-    return unless remote.include? "github.com"
+  def fix_remote_configuration(requested_remote: nil, quiet: false)
+    if requested_remote.present?
+      path.cd do
+        safe_system "git", "remote", "set-url", "origin", requested_remote
+        safe_system "git", "config", "remote.origin.fetch", "+refs/heads/*:refs/remotes/origin/*"
+      end
+      $stderr.ohai "#{name}: changed remote from #{remote} to #{requested_remote}" unless quiet
+    end
 
     current_upstream_head = path.git_origin_branch
-    return if path.git_origin_has_branch? current_upstream_head
+    return if requested_remote.blank? && path.git_origin_has_branch?(current_upstream_head)
 
-    safe_system "git", "-C", path, "fetch", "origin"
+    args = %w[fetch]
+    args << "--quiet" if quiet
+    args << "origin"
+    safe_system "git", "-C", path, *args
     path.git_origin_set_head_auto
 
     new_upstream_head = path.git_origin_branch
+    return if new_upstream_head == old_upstream_head
+
     path.git_rename_branch old: current_upstream_head, new: new_upstream_head
     path.git_branch_set_upstream local: new_upstream_head, origin: new_upstream_head
 
-    ohai "#{name}: changed default branch name from #{current_upstream_head} to #{new_upstream_head}!"
+    return if quiet
+
+    $stderr.ohai "#{name}: changed default branch name from #{current_upstream_head} to #{new_upstream_head}!"
   end
 
   # Uninstall this {Tap}.
@@ -741,12 +761,18 @@ class CoreTap < Tap
   end
 
   # CoreTap never allows shallow clones (on request from GitHub).
-  def install(quiet: false, clone_target: nil, force_auto_update: nil)
+  def install(quiet: false, clone_target: nil, force_auto_update: nil, custom_remote: false)
     remote = Homebrew::EnvConfig.core_git_remote
+    requested_remote = clone_target || default_remote
+
+    # The remote will changed again on `brew update` since remotes for Homebrew/core are mismatched
+    raise TapCoreRemoteMismatchError.new(name, remote, requested_remote) if requested_remote != remote
+
     if remote != default_remote
-      $stderr.puts "HOMEBREW_CORE_GIT_REMOTE set: using #{remote} for Homebrew/core Git remote URL."
+      $stderr.puts "HOMEBREW_CORE_GIT_REMOTE set: using #{remote} for Homebrew/core Git remote."
     end
-    super(quiet: quiet, clone_target: remote, force_auto_update: force_auto_update)
+
+    super(quiet: quiet, clone_target: remote, force_auto_update: force_auto_update, custom_remote: custom_remote)
   end
 
   # @private
diff --git a/Library/Homebrew/test/tap_spec.rb b/Library/Homebrew/test/tap_spec.rb
index f57455027..ae7ef7a25 100644
--- a/Library/Homebrew/test/tap_spec.rb
+++ b/Library/Homebrew/test/tap_spec.rb
@@ -289,6 +289,33 @@ describe Tap do
       }.to raise_error(TapRemoteMismatchError)
     end
 
+    it "raises an error when the remote for Homebrew/core doesn't match HOMEBREW_CORE_GIT_REMOTE" do
+      core_tap = described_class.fetch("Homebrew", "core")
+      wrong_remote = "#{Homebrew::EnvConfig.core_git_remote}-oops"
+      expect {
+        core_tap.install clone_target: wrong_remote
+      }.to raise_error(TapCoreRemoteMismatchError)
+    end
+
+    it "raises an error when run `brew tap --custom-remote` without a custom remote (already installed)" do
+      setup_git_repo
+      already_tapped_tap = described_class.new("Homebrew", "foo")
+      expect(already_tapped_tap).to be_installed
+
+      expect {
+        already_tapped_tap.install clone_target: nil, custom_remote: true
+      }.to raise_error(TapNoCustomRemoteError)
+    end
+
+    it "raises an error when run `brew tap --custom-remote` without a custom remote (not installed)" do
+      not_tapped_tap = described_class.new("Homebrew", "bar")
+      expect(not_tapped_tap).not_to be_installed
+
+      expect {
+        not_tapped_tap.install clone_target: nil, custom_remote: true
+      }.to raise_error(TapNoCustomRemoteError)
+    end
+
     describe "force_auto_update" do
       before do
         setup_git_repo
diff --git a/completions/bash/brew b/completions/bash/brew
index a5027e605..c5b8e4c8b 100644
--- a/completions/bash/brew
+++ b/completions/bash/brew
@@ -1902,6 +1902,7 @@ _brew_tap() {
   case "${cur}" in
     -*)
       __brewcomp "
+      --custom-remote
       --debug
       --force-auto-update
       --full
diff --git a/completions/fish/brew.fish b/completions/fish/brew.fish
index 96b797f46..07facf960 100644
--- a/completions/fish/brew.fish
+++ b/completions/fish/brew.fish
@@ -1288,6 +1288,7 @@ __fish_brew_complete_arg 'style; and not __fish_seen_argument -l formula -l form
 
 
 __fish_brew_complete_cmd 'tap' 'Tap a formula repository'
+__fish_brew_complete_arg 'tap' -l custom-remote -d 'Install or change a tap with a custom remote. Useful for mirrors'
 __fish_brew_complete_arg 'tap' -l debug -d 'Display any debugging information'
 __fish_brew_complete_arg 'tap' -l force-auto-update -d 'Auto-update tap even if it is not hosted on GitHub. By default, only taps hosted on GitHub are auto-updated (for performance reasons)'
 __fish_brew_complete_arg 'tap' -l full -d 'Convert a shallow clone to a full clone without untapping. Taps are only cloned as shallow clones if `--shallow` was originally passed'
diff --git a/completions/zsh/_brew b/completions/zsh/_brew
index cd2342def..8c454ad15 100644
--- a/completions/zsh/_brew
+++ b/completions/zsh/_brew
@@ -1579,6 +1579,7 @@ _brew_style() {
 # brew tap
 _brew_tap() {
   _arguments \
+    '--custom-remote[Install or change a tap with a custom remote. Useful for mirrors]' \
     '--debug[Display any debugging information]' \
     '--force-auto-update[Auto-update tap even if it is not hosted on GitHub. By default, only taps hosted on GitHub are auto-updated (for performance reasons)]' \
     '--full[Convert a shallow clone to a full clone without untapping. Taps are only cloned as shallow clones if `--shallow` was originally passed]' \
diff --git a/docs/Manpage.md b/docs/Manpage.md
index f1b0aa547..efa868051 100644
--- a/docs/Manpage.md
+++ b/docs/Manpage.md
@@ -600,6 +600,8 @@ using protocols other than HTTPS, e.g. SSH, git, HTTP, FTP(S), rsync.
   Fetch tap as a shallow clone rather than a full clone. Useful for continuous integration.
 * `--force-auto-update`:
   Auto-update tap even if it is not hosted on GitHub. By default, only taps hosted on GitHub are auto-updated (for performance reasons).
+* `--custom-remote`:
+  Install or change a tap with a custom remote. Useful for mirrors.
 * `--repair`:
   Migrate tapped formulae from symlink-based to directory-based structure.
 * `--list-pinned`:
diff --git a/manpages/brew.1 b/manpages/brew.1
index 4c6d88d76..7fc6f43a3 100644
--- a/manpages/brew.1
+++ b/manpages/brew.1
@@ -831,6 +831,10 @@ Fetch tap as a shallow clone rather than a full clone\. Useful for continuous in
 Auto\-update tap even if it is not hosted on GitHub\. By default, only taps hosted on GitHub are auto\-updated (for performance reasons)\.
 .
 .TP
+\fB\-\-custom\-remote\fR
+Install or change a tap with a custom remote\. Useful for mirrors\.
+.
+.TP
 \fB\-\-repair\fR
 Migrate tapped formulae from symlink\-based to directory\-based structure\.
 .