diff --git a/.ruby-version b/.ruby-version
new file mode 100644
index 0000000..9cec716
--- /dev/null
+++ b/.ruby-version
@@ -0,0 +1 @@
+3.1.6
diff --git a/CHANGELOG.md b/CHANGELOG.md
index e685ece..4cb64c3 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -3,6 +3,12 @@ All notable changes to this project will be documented in this file.
 The format is based on [Keep a Changelog](https://keepachangelog.com/en/1.0.0/),
 and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.html).
 
+## 0.2.0 - 2024-07-09
+### Added
+- Support special request options for `appraisal_matrix`:
+    - `versions`: An array of version restriction strings.
+    - `step`: The granularity of a release to be included in the matrix. Allowed to be :major, :minor, or :patch.
+
 ## [0.1.0] - 2024-06-26
 ### Added
 - Add an extension to the Appraisal gem that provides an interface for generating a matrix of appraisals.
diff --git a/Gemfile.lock b/Gemfile.lock
index 8afa3d3..29c4817 100644
--- a/Gemfile.lock
+++ b/Gemfile.lock
@@ -1,7 +1,7 @@
 PATH
   remote: .
   specs:
-    appraisal-matrix (0.1.0)
+    appraisal-matrix (0.2.0)
       appraisal (~> 2.2)
 
 GEM
diff --git a/README.md b/README.md
index 10c9778..8a4715e 100644
--- a/README.md
+++ b/README.md
@@ -65,18 +65,27 @@ appraisal_matrix(activesupport: "6.1", sidekiq: "7.0")
 
 In addition to specifying the minimum requested version, users will be able to make additional version requests.
 
-#### Maximum version (Coming soon!)
+#### Additional version restrictions
 
-Include a maximum boundary (inclusive).
+Include additional version boundaries. Either include the requirement strings as an array or pass the `versions` key to the options hash.
 ```ruby
-appraisal_matrix(activesupport: { min: "6.1", max: "7.1" })
+appraisal_matrix(activesupport: [">= 6.1", "< 7.1"])
+appraisal_matrix(activesupport: ["~> 6.0", "!= 6.1.0"])
+appraisal_matrix(activesupport: { versions: ["> 6.1.1"] })
 ```
 
-#### Version step (Coming soon!)
+#### Version step
+
+The default operation is to test against each minor version. You can choose to be more or less inclusive when necessary.
 
 Only test the latest release of each major version.
 ```ruby
-appraisal_matrix(activesupport: { min: "6.1", max: "7.1", step: :major })
+appraisal_matrix(activesupport: { versions: [">= 6.1", "< 7.1"], step: :major })
+```
+
+Or include all patch releases
+```ruby
+appraisal_matrix(activesupport: { versions: [">= 6.1", "< 7.1"], step: :patch })
 ```
 
 ## Development
diff --git a/lib/appraisal/matrix/extensions/appraisal_file.rb b/lib/appraisal/matrix/extensions/appraisal_file.rb
index 4a349aa..f4f7127 100644
--- a/lib/appraisal/matrix/extensions/appraisal_file.rb
+++ b/lib/appraisal/matrix/extensions/appraisal_file.rb
@@ -5,14 +5,34 @@
 
 module Appraisal::Matrix
   module AppraiseFileWithMatrix
-    include RubygemsHelper
 
-    # appraisal_matrix(rails: "6.0")
-    # appraisal_matrix(rails: "6.0", sidekiq: "5")
-    # appraisal_matrix(rails: "6.0", sidekiq: { min: “5.0”, max: “6.0”, step: :major })
-    # appraisal_matrix(rails: "6.0") do
-    #   gem "sqlite3", "~> 2.5"
-    # end
+    class VersionArray
+      SUPPORTED_VERSION_STEPS = [:major, :minor, :patch].freeze
+
+      attr_reader :gem_name, :version_requirements, :step
+
+      def initialize(gem_name:, versions:, step: :minor)
+        SUPPORTED_VERSION_STEPS.include?(step) or raise("Unsupported version step: #{step}")
+
+        @gem_name = gem_name
+        @version_requirements = Gem::Requirement.new(versions)
+        @step = step.to_sym
+      end
+
+      def versions
+        RubygemsHelper.versions_to_test(gem_name, version_requirements, step)
+      end
+    end
+
+    # Define a matrix of appraisals to test against
+    # Expected usage:
+    #   appraisal_matrix(rails: "6.0")
+    #   appraisal_matrix(rails: "> 6.0.3")
+    #   appraisal_matrix(rails: [">= 6.0", "< 7.1"])
+    #   appraisal_matrix(rails: { versions: [">= 6.0", "< 7.1"], step: "major" })
+    #   appraisal_matrix(rails: "6.0") do
+    #     gem "sqlite3", "~> 2.5"
+    #   end
     def appraisal_matrix(**kwargs, &block)
       # names_and_versions_to_test
       # [
@@ -21,14 +41,21 @@ def appraisal_matrix(**kwargs, &block)
       #   [[a, x], [a, y], [a, z]]
       # ]
       names_and_versions_to_test =
-        kwargs.map do |gem_name, version_request|
-          if version_request.is_a?(Hash)
-            raise "TODO: Version request options not implemented yet"
-          else
-            minimum_version = Gem::Version.new(version_request)
-          end
+        kwargs.map do |gem_name, version_options|
+          version_array =
+            case version_options
+            when String
+              parsed_options = version_options.include?(" ") ? [version_options] : [">= #{version_options}"]
+              VersionArray.new(gem_name: gem_name, versions: parsed_options)
+            when Integer, Float
+              VersionArray.new(gem_name: gem_name, versions: [">= #{version_options}"])
+            when Array
+              VersionArray.new(gem_name: gem_name, versions: version_options)
+            when Hash
+              VersionArray.new(gem_name: gem_name, **version_options)
+            end
 
-          versions_to_test(gem_name, minimum_version).map do |version|
+          version_array.versions.map do |version|
             [gem_name, version]
           end
         end
diff --git a/lib/appraisal/matrix/rubygems_helper.rb b/lib/appraisal/matrix/rubygems_helper.rb
index 4a9cd41..16ca29d 100644
--- a/lib/appraisal/matrix/rubygems_helper.rb
+++ b/lib/appraisal/matrix/rubygems_helper.rb
@@ -5,20 +5,46 @@
 
 module Appraisal
   module Matrix
-    module RubygemsHelper
-      def versions_to_test(gem_name, minimum_version)
-        # Generate a set to store the versions to test against 
-        versions_to_test = Set.new
-
-        # Load versions from rubygems api
-        URI.parse("https://rubygems.org/api/v1/versions/#{gem_name}.json").open do |raw_version_data|
-          JSON.parse(raw_version_data.read).each do |version_data|
-            version = Gem::Version.new(version_data['number'])
-            versions_to_test << version.segments[0..1].join('.') if version >= minimum_version && !version.prerelease?
+    class RubygemsHelper
+      class << self
+        # Returns a set of versions to test against for a given gem.
+        #
+        # @param gem_name [String, Symbol] The name of the gem.
+        # @param version_requirement [Gem::Requirement] The version requirement for the gem.
+        # @param step [Symbol] The step value.
+        #
+        # @return [Set] A set of versions to test against.
+        def versions_to_test(gem_name, version_requirement, step)
+          # Generate a set to store the versions to test against 
+          versions_to_test = Set.new
+
+          # Load versions from rubygems api
+          URI.parse("https://rubygems.org/api/v1/versions/#{gem_name}.json").open do |raw_version_data|
+            JSON.parse(raw_version_data.read).each do |version_data|
+              version = Gem::Version.new(version_data['number'])
+              versions_to_test << version_for_step(version, step) if include_version?(version, version_requirement)
+            end
           end
+
+          versions_to_test
         end
 
-        versions_to_test
+        private
+
+        SEGMENT_STEP_SIZES = {
+          major: 1,
+          minor: 2,
+          patch: 3
+        }.freeze
+
+        def version_for_step(version, step)
+          size_for_step = SEGMENT_STEP_SIZES[step] or raise ArgumentError, "unsupported requested version step: #{step}, expected #{SEGMENT_STEP_SIZES.keys}"
+          version.segments.first(size_for_step).join(".")
+        end
+
+        def include_version?(version, version_requirement)
+          !version.prerelease? && version_requirement.satisfied_by?(version)
+        end
       end
     end
   end
diff --git a/lib/appraisal/matrix/version.rb b/lib/appraisal/matrix/version.rb
index 1476589..6b0e693 100644
--- a/lib/appraisal/matrix/version.rb
+++ b/lib/appraisal/matrix/version.rb
@@ -2,6 +2,6 @@
 
 module Appraisal
   module Matrix
-    VERSION = "0.1.0"
+    VERSION = "0.2.0"
   end
 end
diff --git a/spec/appraisal/matrix/extensions/appraisal_file_spec.rb b/spec/appraisal/matrix/extensions/appraisal_file_spec.rb
index 94bde59..2e698ec 100644
--- a/spec/appraisal/matrix/extensions/appraisal_file_spec.rb
+++ b/spec/appraisal/matrix/extensions/appraisal_file_spec.rb
@@ -9,61 +9,136 @@
     subject { appraisal_matrix(**desired_gems) }
 
     context "with a maximum version specified" do
-      let(:desired_gems) { { rails: { min: "6.1", max: "7.0" } } }
+      before do
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:rails, Gem::Requirement.new([">= 6.1", "< 7.1"]), :minor).and_return(["6.1", "7.0"])
+      end
+
+      context "using the keyword argument syntax" do
+        let(:desired_gems) { { rails: { versions: [">= 6.1", "< 7.1"] } } }
+
+        it "creates a matrix of appraisals" do
+          expect(self).to receive(:appraise).with("rails-6_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0") }
+          expect(self).to receive(:appraise).with("rails-7_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0") }
+          subject
+        end
+      end
+
+      context "using the array argument syntax" do
+        let (:desired_gems) { { rails: [">= 6.1", "< 7.1"] } }
 
-      it "is not implemented yet" do
-        expect { subject }.to raise_error("TODO: Version request options not implemented yet")
+        it "creates a matrix of appraisals" do
+          expect(self).to receive(:appraise).with("rails-6_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0") }
+          expect(self).to receive(:appraise).with("rails-7_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0") }
+          subject
+        end
       end
     end
 
-    context "with a step specified" do
-      let(:desired_gems) { { rails: { min: "6.1", step: :major } } }
+    context "requesting major version steps" do
+      let(:desired_gems) { { rails: { versions: [">= 6.1"], step: :major } } }
+
+      before do
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:rails, Gem::Requirement.new([">= 6.1"]), :major).and_return(["6", "7"])
+      end
 
-      it "is not implemented yet" do
-        expect { subject }.to raise_error("TODO: Version request options not implemented yet")
+      it "creates a matrix of appraisals" do
+        expect(self).to receive(:appraise).with("rails-6").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.0") }
+        expect(self).to receive(:appraise).with("rails-7").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0") }
+        subject
       end
     end
 
-    context "for a single gem" do
-      let(:desired_gems) { { rails: "6.1" } }
+    context "requesting patch version steps" do
+      let(:desired_gems) { { rails: { versions: [">= 6.1"], step: :patch } } }
 
       before do
-        allow(self).to receive(:versions_to_test) { ["6.1", "7.0", "7.1"] }
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:rails, Gem::Requirement.new([">= 6.1"]), :patch).and_return(["6.1.0", "6.1.1", "7.0.0", "7.1.0"])
       end
 
-      it "creates a matrix of appraisals including the specified minimum version" do
-        expect(self).to receive(:appraise).with("rails-6_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0") }
-        expect(self).to receive(:appraise).with("rails-7_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0") }
-        expect(self).to receive(:appraise).with("rails-7_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.1.0") }
+      it "creates a matrix of appraisals" do
+        expect(self).to receive(:appraise).with("rails-6_1_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0.0") }
+        expect(self).to receive(:appraise).with("rails-6_1_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.1.0") }
+        expect(self).to receive(:appraise).with("rails-7_0_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0.0") }
+        expect(self).to receive(:appraise).with("rails-7_1_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.1.0.0") }
         subject
       end
+    end
 
-      context "with a block to pass into each appraisal" do
-        it "yields the block to each appraisal" do
-          expect(self).to receive(:appraise).with("rails-6_1").and_yield do |block_scope|
-            expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0")
-            expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
-          end
-          expect(self).to receive(:appraise).with("rails-7_0").and_yield do |block_scope|
-            expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0")
-            expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
-          end
-          expect(self).to receive(:appraise).with("rails-7_1").and_yield do |block_scope|
-            expect(block_scope).to receive(:gem).with(:rails, "~> 7.1.0")
-            expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
-          end
+    context "requesting a step that is not supported" do
+      let(:desired_gems) { { rails: { versions: [">= 6.1"], step: :pizza } } }
+
+      it "raises an error" do
+        expect { subject }.to raise_error("Unsupported version step: pizza")
+      end
+    end
 
-          appraisal_matrix(**desired_gems) { gem "sqlite3", "~> 2.5" }
+    context "default behavior for a single gem" do
+      shared_examples "a matrix of appraisals" do
+        it "creates a matrix of appraisals including the specified minimum version" do
+          expect(self).to receive(:appraise).with("rails-6_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0") }
+          expect(self).to receive(:appraise).with("rails-7_0").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0") }
+          expect(self).to receive(:appraise).with("rails-7_1").and_yield { |block_scope| expect(block_scope).to receive(:gem).with(:rails, "~> 7.1.0") }
+          subject
         end
       end
+
+      before do
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:rails, expected_version_requirement, :minor).and_return(["6.1", "7.0", "7.1"])
+      end
+
+      let(:expected_version_requirement) { Gem::Requirement.new([">= 6.1"]) }
+
+      context "as a string" do
+        let(:desired_gems) { { rails: "6.1" } }
+
+        it_behaves_like "a matrix of appraisals"
+
+        context "with a block to pass into each appraisal" do
+          it "yields the block to each appraisal" do
+            expect(self).to receive(:appraise).with("rails-6_1").and_yield do |block_scope|
+              expect(block_scope).to receive(:gem).with(:rails, "~> 6.1.0")
+              expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
+            end
+            expect(self).to receive(:appraise).with("rails-7_0").and_yield do |block_scope|
+              expect(block_scope).to receive(:gem).with(:rails, "~> 7.0.0")
+              expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
+            end
+            expect(self).to receive(:appraise).with("rails-7_1").and_yield do |block_scope|
+              expect(block_scope).to receive(:gem).with(:rails, "~> 7.1.0")
+              expect(block_scope).to receive(:gem).with("sqlite3", "~> 2.5")
+            end
+
+            appraisal_matrix(**desired_gems) { gem "sqlite3", "~> 2.5" }
+          end
+        end
+      end
+
+      context "as a string with an operator provided" do
+        let(:desired_gems) { { rails: ">= 6.1" } }
+
+        it_behaves_like "a matrix of appraisals"
+      end
+
+      context "as a Float" do
+        let(:desired_gems) { { rails: 6.1 } }
+
+        it_behaves_like "a matrix of appraisals"
+      end
+
+      context "as an Integer" do
+        let(:desired_gems) { { rails: 6 } }
+        let(:expected_version_requirement) { Gem::Requirement.new([">= 6"]) }
+
+        it_behaves_like "a matrix of appraisals"
+      end
     end
 
     context "for multiple gems" do
       let(:desired_gems) { { rails: "6.1", sidekiq: "5" } }
 
       before do
-        allow(self).to receive(:versions_to_test).with(:rails, Gem::Version.new("6.1")).and_return(["6.1", "7.0", "7.1"])
-        allow(self).to receive(:versions_to_test).with(:sidekiq, Gem::Version.new("5")).and_return(["5.0", "6.0"])
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:rails, Gem::Requirement.new([">= 6.1"]), :minor).and_return(["6.1", "7.0", "7.1"])
+        expect(Appraisal::Matrix::RubygemsHelper).to receive(:versions_to_test).with(:sidekiq, Gem::Requirement.new([">= 5"]), :minor).and_return(["5.0", "6.0"])
       end
 
       it "creates a matrix of appraisals including the specified minimum version" do
diff --git a/spec/appraisal/matrix/rubygems_helper_spec.rb b/spec/appraisal/matrix/rubygems_helper_spec.rb
index 37e12d1..81d5333 100644
--- a/spec/appraisal/matrix/rubygems_helper_spec.rb
+++ b/spec/appraisal/matrix/rubygems_helper_spec.rb
@@ -3,13 +3,12 @@
 require_relative "../../../lib/appraisal/matrix/rubygems_helper"
 
 RSpec.describe Appraisal::Matrix::RubygemsHelper do
-  include Appraisal::Matrix::RubygemsHelper
-
   describe "#versions_to_test" do
-    subject { versions_to_test(gem_name, minimum_version) }
+    subject { described_class.versions_to_test(gem_name, version_requirements, step) }
 
-    let(:gem_name) { "rails" }
-    let(:minimum_version) { Gem::Version.new("6.0") }
+    let(:gem_name)             { "rails" }
+    let(:version_requirements) { Gem::Requirement.new(['>= 6.0']) }
+    let(:step)                 { :minor }
     
     let(:parsed_uri) { double("uri") }
     let(:raw_version_data) do
@@ -20,6 +19,7 @@
           { "number" => "6.0.0.rc.1" },
           { "number" => "6.0.0" },
           { "number" => "6.1.0" },
+          { "number" => "6.1.1" },
           { "number" => "7.0.0.rc.1" },
           { "number" => "7.0.0" },
           { "number" => "7.1.0" },
@@ -33,8 +33,32 @@
       allow(parsed_uri).to receive(:open).and_yield(raw_version_data)
     end
 
-    it "returns versions to test" do
-      expect(subject).to eq(Set.new(["6.0", "6.1", "7.0", "7.1"]))
+    it { is_expected.to eq(Set.new(["6.0", "6.1", "7.0", "7.1"])) }
+
+    context "when a maximum version is specified" do
+      let(:version_requirements) { Gem::Requirement.new(['>= 6.0', '< 7.0']) }
+
+      it { is_expected.to eq(Set.new(["6.0", "6.1"])) }
+    end
+
+    context "when the step is :major" do
+      let(:step) { :major }
+
+      it { is_expected.to eq(Set.new(["6", "7"])) }
+    end
+
+    context "when the step is :patch" do
+      let(:step) { :patch }
+
+      it { is_expected.to eq(Set.new(["6.0.0", "6.1.0", "6.1.1", "7.0.0", "7.1.0", "7.1.1"])) }
+    end
+
+    context "when the step is anything else" do
+      let(:step) { :pizza }
+
+      it "raises an error" do
+        expect { subject }.to raise_error("unsupported requested version step: pizza, expected [:major, :minor, :patch]")
+      end
     end
   end
 end