diff --git a/.github/workflows/IntegrationTestChainRules.yml b/.github/workflows/IntegrationTestChainRules.yml
index 5b7d047a7..ae61d5a7e 100644
--- a/.github/workflows/IntegrationTestChainRules.yml
+++ b/.github/workflows/IntegrationTestChainRules.yml
@@ -1,4 +1,4 @@
-name: IntegrationTestChainRules 
+name: IntegrationTest
 on:
   push:
     branches: [master]
@@ -7,12 +7,22 @@ on:
 
 jobs:
   test:
-    name: Julia v${{ matrix.julia-version }} - ${{ matrix.os }}
+    name: ${{ matrix.package.repo }}
     runs-on: ${{ matrix.os }}
     strategy:
+      fail-fast: false
       matrix:
         julia-version: [1]
         os: [ubuntu-latest]
+        package:
+          - {user: JuliaDiff, repo: ChainRules.jl}
+          - {user: JuliaMath, repo: SpecialFunctions.jl}
+          - {user: invenia, repo: BlockDiagonals.jl}
+          - {user: invenia, repo: PDMatsExtras.jl}
+          - {user: chrisbrahms, repo: Hankel.jl}
+          - {user: SciML, repo: DiffEqBase.jl}
+          - {user: dfdx, repo: Yota.jl}
+
     steps:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@v1
@@ -20,11 +30,26 @@ jobs:
           version: ${{ matrix.julia-version }}
           arch: x64
       - uses: julia-actions/julia-buildpkg@latest
-      - name: Clone ChainRules
+      - name: Clone Downstream
         uses: actions/checkout@v2
         with:
-          repository: JuliaDiff/ChainRules.jl
-          path: "ChainRules.jl"
-      - name: Run the tests
-        run: julia --project="ChainRules.jl" -e "using Pkg; Pkg.develop(PackageSpec(path=\"./\")); Pkg.update(); Pkg.test()"
-        shell: bash
+          repository: ${{ matrix.package.user }}/${{ matrix.package.repo }}
+          path: downstream
+      - name: Load this and run the downstream tests
+        shell: julia --project=downstream {0}
+        run: |
+          using Pkg
+          try
+            # force it to use this PR's version of the package
+            Pkg.develop(PackageSpec(path="."))  # resolver may fail with main deps
+            Pkg.update()
+            Pkg.test()  # resolver may fail with test time deps 
+          catch err
+            err isa Pkg.Resolve.ResolverError || rethrow()
+            # If we can't resolve that means this is incompatible by SemVer and this is fine
+            # It means we marked this as a breaking change, so we don't need to worry about
+            # Mistakenly introducing a breaking change, as we have intentionally made one
+
+            @info "Not compatible with this release. No problem." exception=err
+            exit(0)  # Exit immediately, as a success
+          end