diff --git a/Library/Homebrew/dev-cmd/bump-cask-pr.rb b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
index cc235e9af9d3c..4f520d67c1616 100644
--- a/Library/Homebrew/dev-cmd/bump-cask-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-cask-pr.rb
@@ -93,6 +93,8 @@ def run
             #{Formatter.url("#{cask.tap.remote}/blob/master/.github/autobump.txt")}
         EOS
 
+        odie "You have too many PRs open: close or merge some first!" if GitHub.too_many_open_prs?(cask.tap)
+
         new_version = BumpVersionParser.new(
           general: args.version,
           intel:   args.version_intel,
diff --git a/Library/Homebrew/dev-cmd/bump-formula-pr.rb b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
index 6ba96dd76b225..2c972aab94ab7 100644
--- a/Library/Homebrew/dev-cmd/bump-formula-pr.rb
+++ b/Library/Homebrew/dev-cmd/bump-formula-pr.rb
@@ -120,6 +120,8 @@ def run
             #{Formatter.url("#{formula.tap.remote}/blob/master/.github/autobump.txt")}
         EOS
 
+        odie "You have too many PRs open: close or merge some first!" if GitHub.too_many_open_prs?(formula.tap)
+
         formula_spec = formula.stable
         odie "#{formula}: no stable specification found!" if formula_spec.blank?
 
diff --git a/Library/Homebrew/dev-cmd/bump.rb b/Library/Homebrew/dev-cmd/bump.rb
index cc19ca70be6c7..3de0bd860a4ef 100644
--- a/Library/Homebrew/dev-cmd/bump.rb
+++ b/Library/Homebrew/dev-cmd/bump.rb
@@ -499,6 +499,10 @@ def retrieve_and_display_info_and_open_pr(formula_or_cask, name, repositories, a
 
         return unless args.open_pr?
 
+        if GitHub.too_many_open_prs?(formula_or_cask.tap)
+          odie "You have too many PRs open: close or merge some first!"
+        end
+
         if repology_latest.is_a?(Version) &&
            repology_latest > current_version.general &&
            repology_latest > new_version.general &&
diff --git a/Library/Homebrew/utils/github.rb b/Library/Homebrew/utils/github.rb
index 5117f58b1268e..17f6ec40b0209 100644
--- a/Library/Homebrew/utils/github.rb
+++ b/Library/Homebrew/utils/github.rb
@@ -863,4 +863,60 @@ def self.count_repo_commits(nwo, user, args, max: nil)
 
     [author_count, committer_count]
   end
+
+  MAXIMUM_OPEN_PRS = 15
+
+  sig { params(tap: T.nilable(Tap)).returns(T::Boolean) }
+  def self.too_many_open_prs?(tap)
+    # We don't enforce unofficial taps.
+    return false if tap.nil? || !tap.official?
+
+    # BrewTestBot can open as many PRs as it wants.
+    return false if ENV["HOMEBREW_TEST_BOT_AUTOBUMP"].present?
+
+    odie "Cannot count PRs, HOMEBREW_NO_GITHUB_API set!" if Homebrew::EnvConfig.no_github_api?
+
+    query = <<~EOS
+      query {
+        viewer {
+          login
+          pullRequests(first: 100, states: OPEN) {
+            nodes {
+              headRepositoryOwner {
+                login
+              }
+            }
+            pageInfo {
+              hasNextPage
+            }
+          }
+        }
+      }
+    EOS
+    graphql_result = API.open_graphql(query)
+    puts
+
+    github_user = graphql_result.dig("viewer", "login")
+    odie "Cannot count PRs, cannot get GitHub username from GraphQL API!" if github_user.blank?
+
+    # BrewTestBot can open as many PRs as it wants.
+    return false if github_user.casecmp("brewtestbot").zero?
+
+    prs = graphql_result.dig("viewer", "pullRequests", "nodes")
+    more_graphql_data = graphql_result.dig("viewer", "pullRequests", "pageInfo", "hasNextPage")
+    return false if !more_graphql_data && prs.length < MAXIMUM_OPEN_PRS
+
+    homebrew_prs_count = graphql_result.dig("viewer", "pullRequests", "nodes").count do |pr|
+      pr["headRepositoryOwner"]["login"] == "Homebrew"
+    end
+    return true if homebrew_prs_count >= MAXIMUM_OPEN_PRS
+    return false unless more_graphql_data
+    return false if tap.nil?
+
+    url = "#{API_URL}/repos/#{tap.full_name}/issues?state=open&creator=#{github_user}"
+    rest_result = API.open_rest(url)
+    repo_prs_count = rest_result.count { |issue_or_pr| issue_or_pr.key?("pull_request") }
+
+    repo_prs_count >= MAXIMUM_OPEN_PRS
+  end
 end