diff --git a/Library/Homebrew/test/utils/pypi_spec.rb b/Library/Homebrew/test/utils/pypi_spec.rb
new file mode 100644
index 0000000000..021a2215c8
--- /dev/null
+++ b/Library/Homebrew/test/utils/pypi_spec.rb
@@ -0,0 +1,171 @@
+# typed: false
+# frozen_string_literal: true
+
+require "utils/pypi"
+
+describe PyPI do
+  let(:package_url) do
+    "https://files.pythonhosted.org/packages/b0/3f/2e1dad67eb172b6443b5eb37eb885a054a55cfd733393071499514140282/"\
+    "snakemake-5.29.0.tar.gz"
+  end
+  let(:old_package_url) do
+    "https://files.pythonhosted.org/packages/6f/c4/da52bfdd6168ea46a0fe2b7c983b6c34c377a8733ec177cc00b197a96a9f/"\
+    "snakemake-5.28.0.tar.gz"
+  end
+
+  describe PyPI::Package do
+    let(:package_checksum) { "47417307d08ecb0707b3b29effc933bd63d8c8e3ab15509c62b685b7614c6568" }
+    let(:old_package_checksum) { "2367ce91baf7f8fa7738d33aff9670ffdf5410bbac49aeb209f73b45a3425046" }
+
+    let(:package) { described_class.new("snakemake") }
+    let(:package_with_version) { described_class.new("snakemake==5.28.0") }
+    let(:package_with_different_version) { described_class.new("snakemake==5.29.0") }
+    let(:package_with_extra) { described_class.new("snakemake[foo]") }
+    let(:package_with_extra_and_version) { described_class.new("snakemake[foo]==5.28.0") }
+    let(:package_from_url) { described_class.new(package_url, is_url: true) }
+    let(:other_package) { described_class.new("virtualenv==20.2.0") }
+
+    describe "initialize" do
+      it "initializes name" do
+        expect(described_class.new("foo").name).to eq "foo"
+      end
+
+      it "initializes name with extra" do
+        expect(described_class.new("foo[bar]").name).to eq "foo"
+      end
+
+      it "initializes extra" do
+        expect(described_class.new("foo[bar]").extras).to eq ["bar"]
+      end
+
+      it "initializes multiple extras" do
+        expect(described_class.new("foo[bar,baz]").extras).to eq ["bar", "baz"]
+      end
+
+      it "initializes name with version" do
+        expect(described_class.new("foo==1.2.3").name).to eq "foo"
+      end
+
+      it "initializes version" do
+        expect(described_class.new("foo==1.2.3").version).to eq "1.2.3"
+      end
+
+      it "initializes extra with version" do
+        expect(described_class.new("foo[bar]==1.2.3").extras).to eq ["bar"]
+      end
+
+      it "initializes multiple extras with version" do
+        expect(described_class.new("foo[bar,baz]==1.2.3").extras).to eq ["bar", "baz"]
+      end
+
+      it "initializes version with extra" do
+        expect(described_class.new("foo[bar]==1.2.3").version).to eq "1.2.3"
+      end
+
+      it "initializes version with multiple extras" do
+        expect(described_class.new("foo[bar,baz]==1.2.3").version).to eq "1.2.3"
+      end
+
+      it "initializes name from url" do
+        expect(described_class.new(package_url, is_url: true).name).to eq "snakemake"
+      end
+
+      it "initializes version from url" do
+        expect(described_class.new(package_url, is_url: true).version).to eq "5.29.0"
+      end
+    end
+
+    describe ".pypi_info", :needs_network do
+      it "gets pypi info from a package name" do
+        expect(package.pypi_info.first).to eq "snakemake"
+      end
+
+      it "gets pypi info from a package name and specified version" do
+        expect(package.pypi_info(version: "5.29.0")).to eq ["snakemake", package_url, package_checksum, "5.29.0"]
+      end
+
+      it "gets pypi info from a package name with extra" do
+        expect(package_with_extra.pypi_info.first).to eq "snakemake"
+      end
+
+      it "gets pypi info from a package name and version" do
+        expect(package_with_version.pypi_info).to eq ["snakemake", old_package_url, old_package_checksum, "5.28.0"]
+      end
+
+      it "gets pypi info from a package name with overriden version" do
+        expected_result = ["snakemake", package_url, package_checksum, "5.29.0"]
+        expect(package_with_version.pypi_info(version: "5.29.0")).to eq expected_result
+      end
+
+      it "gets pypi info from a package name, extras, and version" do
+        expected_result = ["snakemake", old_package_url, old_package_checksum, "5.28.0"]
+        expect(package_with_extra_and_version.pypi_info).to eq expected_result
+      end
+
+      it "gets pypi info from a url" do
+        expect(package_from_url.pypi_info).to eq ["snakemake", package_url, package_checksum, "5.29.0"]
+      end
+
+      it "gets pypi info from a url with overriden version" do
+        expected_result = ["snakemake", old_package_url, old_package_checksum, "5.28.0"]
+        expect(package_from_url.pypi_info(version: "5.28.0")).to eq expected_result
+      end
+    end
+
+    describe ".to_s" do
+      it "returns string representation of package name" do
+        expect(package.to_s).to eq "snakemake"
+      end
+
+      it "returns string representation of package with version" do
+        expect(package_with_version.to_s).to eq "snakemake==5.28.0"
+      end
+
+      it "returns string representation of package with extra" do
+        expect(package_with_extra.to_s).to eq "snakemake[foo]"
+      end
+
+      it "returns string representation of package with extra and version" do
+        expect(package_with_extra_and_version.to_s).to eq "snakemake[foo]==5.28.0"
+      end
+
+      it "returns string representation of package from url" do
+        expect(package_from_url.to_s).to eq "snakemake==5.29.0"
+      end
+    end
+
+    describe ".same_package?" do
+      it "returns false for different packages" do
+        expect(package.same_package?(other_package)).to eq false
+      end
+
+      it "returns true for the same package" do
+        expect(package.same_package?(package_with_version)).to eq true
+      end
+
+      it "returns true for the same package with different versions" do
+        expect(package_with_version.same_package?(package_with_different_version)).to eq true
+      end
+    end
+
+    describe "<=>" do
+      it "returns -1" do
+        expect(package <=> other_package).to eq((-1))
+      end
+
+      it "returns 0" do
+        expect(package <=> package_with_version).to eq 0
+      end
+
+      it "returns 1" do
+        expect(other_package <=> package_with_extra_and_version).to eq 1
+      end
+    end
+  end
+
+  describe "update_pypi_url", :needs_network do
+    it "updates url to new version" do
+      expect(described_class.update_pypi_url(old_package_url, "5.29.0")).to eq package_url
+    end
+  end
+end
diff --git a/Library/Homebrew/utils/pypi.rb b/Library/Homebrew/utils/pypi.rb
index 4c15a03140..d69291b069 100644
--- a/Library/Homebrew/utils/pypi.rb
+++ b/Library/Homebrew/utils/pypi.rb
@@ -5,6 +5,8 @@
 #
 # @api private
 module PyPI
+  extend T::Sig
+
   module_function
 
   PYTHONHOSTED_URL_PREFIX = "https://files.pythonhosted.org/packages/"
@@ -12,45 +14,119 @@ module PyPI
 
   @pipgrip_installed = nil
 
-  def url_to_pypi_package_name(url)
-    return unless url.start_with? PYTHONHOSTED_URL_PREFIX
+  # PyPI Package
+  #
+  # @api private
+  class Package
+    extend T::Sig
 
-    File.basename(url).match(/^(.+)-[a-z\d.]+$/)[1]
+    attr_accessor :name
+    attr_accessor :extras
+    attr_accessor :version
+
+    sig { params(package_string: String, is_url: T::Boolean).void }
+    def initialize(package_string, is_url: false)
+      @pypi_info = nil
+
+      if is_url
+        unless package_string.start_with?(PYTHONHOSTED_URL_PREFIX) &&
+               match = File.basename(package_string).match(/^(.+)-([a-z\d.]+?)(?:.tar.gz|.zip)$/)
+          raise ArgumentError, "package should be a valid PyPI url"
+        end
+
+        @name = match[1]
+        @version = match[2]
+        return
+      end
+
+      @name = package_string
+      @name, @version = @name.split("==") if @name.include? "=="
+
+      return unless match = @name.match(/^(.*?)\[(.+)\]$/)
+
+      @name = match[1]
+      @extras = match[2].split ","
+    end
+
+    # Get name, URL, SHA-256 checksum, and latest version for a given PyPI package.
+    sig { params(version: T.nilable(T.any(String, Version))).returns(T.nilable(T::Array[String])) }
+    def pypi_info(version: nil)
+      return @pypi_info if @pypi_info.present? && version.blank?
+
+      version ||= @version
+      metadata_url = if version.present?
+        "https://pypi.org/pypi/#{@name}/#{version}/json"
+      else
+        "https://pypi.org/pypi/#{@name}/json"
+      end
+      out, _, status = curl_output metadata_url, "--location"
+
+      return unless status.success?
+
+      begin
+        json = JSON.parse out
+      rescue JSON::ParserError
+        return
+      end
+
+      sdist = json["urls"].find { |url| url["packagetype"] == "sdist" }
+      return json["info"]["name"] if sdist.nil?
+
+      @pypi_info = [json["info"]["name"], sdist["url"], sdist["digests"]["sha256"], json["info"]["version"]]
+    end
+
+    sig { returns(T::Boolean) }
+    def valid_pypi_package?
+      info = pypi_info
+      info.present? && info.is_a?(Array)
+    end
+
+    sig { returns(String) }
+    def to_s
+      out = @name
+      out += "[#{@extras.join(",")}]" if @extras.present?
+      out += "==#{@version}" if @version.present?
+      out
+    end
+
+    sig { params(other: Package).returns(T::Boolean) }
+    def same_package?(other)
+      @name.tr("_", "-") == other.name.tr("_", "-")
+    end
+
+    # Compare only names so we can use .include? on a Package array
+    sig { params(other: Package).returns(T::Boolean) }
+    def ==(other)
+      same_package?(other)
+    end
+
+    sig { params(other: Package).returns(T.nilable(Integer)) }
+    def <=>(other)
+      @name <=> other.name
+    end
   end
 
+  sig { params(url: String, version: T.any(String, Version)).returns(T.nilable(String)) }
   def update_pypi_url(url, version)
-    package = url_to_pypi_package_name url
-    return if package.nil?
+    package = Package.new url, is_url: true
 
-    _, url = get_pypi_info(package, version)
+    _, url = package.pypi_info(version: version)
     url
   end
 
-  # Get name, URL, SHA-256 checksum, and latest version for a given PyPI package.
-  def get_pypi_info(package, version = nil)
-    package = package.split("[").first
-    metadata_url = if version.present?
-      "https://pypi.org/pypi/#{package}/#{version}/json"
-    else
-      "https://pypi.org/pypi/#{package}/json"
-    end
-    out, _, status = curl_output metadata_url, "--location"
-
-    return unless status.success?
-
-    begin
-      json = JSON.parse out
-    rescue JSON::ParserError
-      return
-    end
-
-    sdist = json["urls"].find { |url| url["packagetype"] == "sdist" }
-    return json["info"]["name"] if sdist.nil?
-
-    [json["info"]["name"], sdist["url"], sdist["digests"]["sha256"], json["info"]["version"]]
-  end
-
   # Return true if resources were checked (even if no change).
+  sig do
+    params(
+      formula:                  Formula,
+      version:                  T.nilable(String),
+      package_name:             T.nilable(String),
+      extra_packages:           T.nilable(T::Array[String]),
+      exclude_packages:         T.nilable(T::Array[String]),
+      print_only:               T::Boolean,
+      silent:                   T::Boolean,
+      ignore_non_pypi_packages: T::Boolean,
+    ).returns(T.nilable(T::Boolean))
+  end
   def update_python_resources!(formula, version: nil, package_name: nil, extra_packages: nil, exclude_packages: nil,
                                print_only: false, silent: false, ignore_non_pypi_packages: false)
 
@@ -73,12 +149,17 @@ module PyPI
       end
     end
 
-    version ||= formula.version if package_name.blank?
-    package_name ||= url_to_pypi_package_name formula.stable.url
-    extra_packages ||= []
-    exclude_packages ||= []
+    main_package = if package_name.present?
+      Package.new(package_name)
+    else
+      begin
+        Package.new(formula.stable.url, is_url: true)
+      rescue ArgumentError
+        nil
+      end
+    end
 
-    if package_name.blank?
+    if main_package.blank?
       return if ignore_non_pypi_packages
 
       odie <<~EOS
@@ -87,76 +168,81 @@ module PyPI
       EOS
     end
 
-    input_package_names = { package_name => version }
-    extra_packages.each do |extra|
-      extra_name, extra_version = extra.split "=="
+    unless main_package.valid_pypi_package?
+      return if ignore_non_pypi_packages
 
-      if input_package_names.key?(extra_name) && input_package_names[extra_name] != extra_version
-        odie "Conflicting versions specified for the `#{extra_name}` package: "\
-              "#{input_package_names[extra_name]}, #{extra_version}"
+      odie "\"#{main_package}\" is not available on PyPI."
+    end
+
+    main_package.version = version if version.present?
+
+    extra_packages = (extra_packages || []).map { |p| Package.new p }
+    exclude_packages = (exclude_packages || []).map { |p| Package.new p }
+
+    input_packages = [main_package]
+    extra_packages.each do |extra_package|
+      if !extra_package.valid_pypi_package? && !ignore_non_pypi_packages
+        odie "\"#{extra_package}\" is not available on PyPI."
       end
 
-      input_package_names[extra_name] = extra_version
+      input_packages.each do |existing_package|
+        if existing_package.same_package?(extra_package) && existing_package.version != extra_package.version
+          odie "Conflicting versions specified for the `#{extra_package.name}` package: "\
+                "#{existing_package.version}, #{extra_package.version}"
+        end
+      end
+
+      input_packages << extra_package unless input_packages.include? extra_package
     end
 
-    input_package_names.each do |name, package_version|
-      name = name.split("[").first
-      next if get_pypi_info(name, package_version).present?
-
-      version_string = " at version #{package_version}" if package_version.present?
-      odie "\"#{name}\"#{version_string} is not available on PyPI." unless ignore_non_pypi_packages
-    end
-
-    non_pypi_resources = formula.resources.reject do |resource|
-      resource.url.start_with? PYTHONHOSTED_URL_PREFIX
-    end
-
-    if non_pypi_resources.present? && !print_only
-      odie "\"#{formula.name}\" contains non-PyPI resources. Please update the resources manually."
+    formula.resources.each do |resource|
+      if !print_only && !resource.url.start_with?(PYTHONHOSTED_URL_PREFIX)
+        odie "\"#{formula.name}\" contains non-PyPI resources. Please update the resources manually."
+      end
     end
 
     @pipgrip_installed ||= Formula["pipgrip"].any_version_installed?
     odie '"pipgrip" must be installed (`brew install pipgrip`)' unless @pipgrip_installed
 
-    found_packages = {}
-    input_package_names.each do |name, package_version|
-      pypi_package_string = if package_version.present?
-        "#{name}==#{package_version}"
-      else
-        name
-      end
-
-      ohai "Retrieving PyPI dependencies for \"#{pypi_package_string}\"..." if !print_only && !silent
-      pipgrip_output = Utils.popen_read Formula["pipgrip"].bin/"pipgrip", "--json", "--no-cache-dir",
-                                        pypi_package_string
+    found_packages = []
+    input_packages.each do |package|
+      ohai "Retrieving PyPI dependencies for \"#{package}\"..." if !print_only && !silent
+      pipgrip_output = Utils.popen_read Formula["pipgrip"].bin/"pipgrip", "--json", "--no-cache-dir", package.to_s
       unless $CHILD_STATUS.success?
         odie <<~EOS
-          Unable to determine dependencies for \"#{name}\" because of a failure when running
-          `pipgrip --json --no-cache-dir #{pypi_package_string}`.
+          Unable to determine dependencies for \"#{package}\" because of a failure when running
+          `pipgrip --json --no-cache-dir #{package}`.
           Please update the resources for \"#{formula.name}\" manually.
         EOS
       end
 
-      found_packages.merge!(JSON.parse(pipgrip_output).to_h) do |conflicting_package, old_version, new_version|
-        next old_version if old_version == new_version
+      JSON.parse(pipgrip_output).to_h.each do |new_name, new_version|
+        new_package = Package.new("#{new_name}==#{new_version}")
 
-        odie "Conflicting versions found for the `#{conflicting_package}` resource: #{old_version}, #{new_version}"
+        found_packages.each do |existing_package|
+          if existing_package.same_package?(new_package) && existing_package.version != new_package.version
+            odie "Conflicting versions found for the `#{new_package.name}` resource: "\
+                 "#{existing_package.version}, #{new_package.version}"
+          end
+        end
+
+        found_packages << new_package unless found_packages.include? new_package
       end
     end
 
     # Remove extra packages that may be included in pipgrip output
-    exclude_list = %W[#{package_name.split("[").first.downcase} argparse pip setuptools wheel wsgiref]
+    exclude_list = %W[#{main_package.name} argparse pip setuptools wheel wsgiref].map { |p| Package.new p }
     found_packages.delete_if { |package| exclude_list.include? package }
 
     new_resource_blocks = ""
-    found_packages.sort.each do |package, package_version|
+    found_packages.sort.each do |package|
       if exclude_packages.include? package
-        ohai "Excluding \"#{package}==#{package_version}\"" if !print_only && !silent
+        ohai "Excluding \"#{package}\"" if !print_only && !silent
         next
       end
 
-      ohai "Getting PyPI info for \"#{package}==#{package_version}\"" if !print_only && !silent
-      name, url, checksum = get_pypi_info package, package_version
+      ohai "Getting PyPI info for \"#{package}\"" if !print_only && !silent
+      name, url, checksum = package.pypi_info
       # Fail if unable to find name, url or checksum for any resource
       if name.blank?
         odie "Unable to resolve some dependencies. Please update the resources for \"#{formula.name}\" manually."