diff --git a/.github/workflows/header_checks.yml b/.github/workflows/header_checks.yml
new file mode 100644
index 00000000000..fb84287946b
--- /dev/null
+++ b/.github/workflows/header_checks.yml
@@ -0,0 +1,65 @@
+name: Header checks
+
+on:
+  pull_request:
+    branches: [ develop, master ]
+  push:
+    branches: [ develop, master ]
+    paths-ignore:
+      - 'doygen/**'
+      - 'hooks/**'
+      - 'licenses/**'
+      - 'LICENSE.md'
+      - 'README.md'
+      - 'RELEASE-NOTES.txt'
+
+jobs:
+  windows:
+    name: Windows
+    runs-on: windows-latest
+
+    steps:
+    - uses: n1hility/cancel-previous-runs@v2
+      with:
+        token: ${{ secrets.GITHUB_TOKEN }}
+        workflow: c-cpp.yml
+      if: "!startsWith(github.ref, 'refs/tags/') && github.ref != 'refs/heads/master' && github.ref != 'refs/heads/develop'"
+  
+    - uses: actions/checkout@v2
+    - uses: actions/setup-python@v2
+      with:
+        python-version: '2.x'
+    
+    - name: Print g++/mingw32-make version and path
+      run: |
+        g++ --version
+        Get-Command g++ | Select-Object -ExpandProperty Definition
+        mingw32-make --version
+        Get-Command mingw32-make | Select-Object -ExpandProperty Definition
+      shell: powershell
+
+    - name: Build Math libs
+      shell: powershell
+      run: mingw32-make -f make/standalone math-libs
+      
+    - name: Run header tests
+      shell: powershell
+      run: make -j2 test-headers
+
+  opencl:
+    name: OpenCL
+    runs-on: ubuntu-latest
+
+    steps:
+    - uses: n1hility/cancel-previous-runs@v2
+      with:
+        token: ${{ secrets.GITHUB_TOKEN }}
+        workflow: c-cpp.yml
+      if: "!startsWith(github.ref, 'refs/tags/') && github.ref != 'refs/heads/master' && github.ref != 'refs/heads/develop'"
+  
+    - uses: actions/checkout@v2
+          
+    - name: Run header tests
+      run: |
+        echo "STAN_OPENCL=true" > make/local
+        make -j2 test-headers
\ No newline at end of file
diff --git a/Jenkinsfile b/Jenkinsfile
index 264abf81971..527bb2d0eae 100644
--- a/Jenkinsfile
+++ b/Jenkinsfile
@@ -61,6 +61,7 @@ pipeline {
         string(defaultValue: '', name: 'stan_pr', description: 'PR to test Stan upstream against e.g. PR-630')
         booleanParam(defaultValue: false, name: 'withRowVector', description: 'Run additional distribution tests on RowVectors (takes 5x as long)')
         booleanParam(defaultValue: false, name: 'gpu_async', description: 'Run the OpenCL tests on both a sync (AMD) GPU and an async (NVIDIA) one.')
+        booleanParam(defaultValue: false, name: 'run_win_tests', description: 'Run full unit tests on Windows.')
     }
     options {
         skipDefaultCheckout()
@@ -220,6 +221,7 @@ pipeline {
                     !skipRemainingStages
                 }
             }
+            failFast true
             parallel {
                 stage('MPI tests') {
                     agent { label 'linux && mpi' }
@@ -243,7 +245,6 @@ pipeline {
                         sh "echo STAN_OPENCL=true>> make/local"
                         sh "echo OPENCL_PLATFORM_ID=0>> make/local"
                         sh "echo OPENCL_DEVICE_ID=${OPENCL_DEVICE_ID}>> make/local"
-                        sh "make -j${env.PARALLEL} test-headers"
                         runTests("test/unit/math/opencl")
                         runTests("test/unit/math/prim/fun/gp_exp_quad_cov_test")
                         runTests("test/unit/math/prim/fun/mdivide_left_tri_test")
@@ -268,7 +269,6 @@ pipeline {
                         sh "echo STAN_OPENCL=true>> make/local"
                         sh "echo OPENCL_PLATFORM_ID=0>> make/local"
                         sh "echo OPENCL_DEVICE_ID=${OPENCL_DEVICE_ID}>> make/local"
-                        sh "make -j${env.PARALLEL} test-headers"
                         runTests("test/unit/math/opencl")
                         runTests("test/unit/math/prim/fun/gp_exp_quad_cov_test")
                         runTests("test/unit/math/prim/fun/mdivide_left_tri_test")
@@ -310,79 +310,48 @@ pipeline {
                     agent any
                     steps {
                         script {
-                            if (isUnix()) {
-                                deleteDir()
-                                unstash 'MathSetup'
-                                sh "echo CXX=${env.CXX} -Werror > make/local"
-                                sh "echo CPPFLAGS+=-DSTAN_THREADS >> make/local"
-                                sh "export STAN_NUM_THREADS=4"
+                            deleteDir()
+                            unstash 'MathSetup'
+                            sh "echo CXX=${env.CXX} -Werror > make/local"
+                            sh "echo STAN_THREADS=true >> make/local"
+                            sh "export STAN_NUM_THREADS=4"
+                            if (isBranch('develop') || isBranch('master')) {
+                                runTests("test/unit")
+                                sh "find . -name *_test.xml | xargs rm"
+                            } else {
                                 runTests("test/unit -f thread")
                                 sh "find . -name *_test.xml | xargs rm"
                                 runTests("test/unit -f map_rect")
                                 sh "find . -name *_test.xml | xargs rm"
-                                runTests("test/unit -f reduce_sum")                            
-                            } else {
-                                deleteDirWin()
-                                unstash 'MathSetup'
-                                bat "echo CXX=${env.CXX} -Werror > make/local"
-                                bat "echo CXXFLAGS+=-DSTAN_THREADS >> make/local"
-                                runTestsWin("test/unit -f thread", false)
-                                runTestsWin("test/unit -f map_rect", false)
-                                runTestsWin("test/unit -f reduce_sum", false)
+                                runTests("test/unit -f reduce_sum")
                             }
                         }                      
                     }
                     post { always { retry(3) { deleteDir() } } }
                 }
                 stage('Windows Headers & Unit') {
+                    when {
+                        allOf {
+                            anyOf {
+                                branch 'develop'
+                                branch 'master'
+                                expression { params.run_win_tests }
+                            }
+                            expression {
+                                !skipRemainingStages
+                            }
+                        }
+                    }
                     agent { label 'windows' }
                     steps {
                         deleteDirWin()
                         unstash 'MathSetup'
                         bat "mingw32-make.exe -f make/standalone math-libs"
-                        bat "mingw32-make -j${env.PARALLEL} test-headers"
                         runTestsWin("test/unit", false, true)
                     }
                 }
             }
         }
-        stage('Additional merge tests') {
-            when {
-                allOf {
-                    anyOf {
-                        branch 'develop'
-                        branch 'master'
-                    }
-                    expression {
-                        !skipRemainingStages
-                    }
-                }
-            }
-            parallel {
-                stage('Linux Unit with Threading') {
-                    agent { label 'linux' }
-                    steps {
-                        deleteDir()
-                        unstash 'MathSetup'
-                        sh "echo CXX=${GCC} >> make/local"
-                        sh "echo CXXFLAGS=-DSTAN_THREADS >> make/local"
-                        runTests("test/unit")
-                    }
-                    post { always { retry(3) { deleteDir() } } }
-                }
-                stage('Mac Unit with Threading') {
-                    agent  { label 'osx' }
-                    steps {
-                        deleteDir()
-                        unstash 'MathSetup'
-                        sh "echo CC=${env.CXX} -Werror > make/local"
-                        sh "echo CXXFLAGS+=-DSTAN_THREADS >> make/local"
-                        runTests("test/unit")
-                    }
-                    post { always { retry(3) { deleteDir() } } }
-                }
-            }
-        }
         stage('Upstream tests') {
             when {
                 allOf {