diff --git a/.github/workflows/IntegrationTest.yml b/.github/workflows/IntegrationTest.yml
index a0dca43..6b9656e 100644
--- a/.github/workflows/IntegrationTest.yml
+++ b/.github/workflows/IntegrationTest.yml
@@ -7,7 +7,7 @@ on:
 
 jobs:
   test:
-    name: ${{ matrix.package.repo }}
+    name: ${{ matrix.package.name }}
     runs-on: ${{ matrix.os }}
     strategy:
       fail-fast: false
@@ -15,30 +15,31 @@ jobs:
         julia-version: [1]
         os: [ubuntu-latest]
         package:
-          - {user: JuliaDiff, repo: ChainRules.jl}
-          - {user: JuliaMath, repo: SpecialFunctions.jl}
-          - {user: invenia, repo: BlockDiagonals.jl}
+          - {user: JuliaDiff, name: ChainRules}
+          - {user: JuliaMath, name: SpecialFunctions}
+          - {user: invenia, name: BlockDiagonals}
     steps:
       - uses: actions/checkout@v2
       - uses: julia-actions/setup-julia@v1
         with:
           version: ${{ matrix.julia-version }}
           arch: x64
+      - uses: julia-actions/cache@v3
       - uses: julia-actions/julia-buildpkg@latest
       - name: Clone Downstream
         uses: actions/checkout@v2
         with:
-          repository: ${{ matrix.package.user }}/${{ matrix.package.repo }}
+          repository: ${{ matrix.package.user }}/${{ matrix.package.name }}.jl
           path: downstream
       - name: Load this and run the downstream tests
-        shell: julia --project=downstream {0}
+        shell: julia --project=@temp {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.develop([PackageSpec(path="."), PackageSpec(path="downstream")])  # resolver may fail with main deps
             Pkg.update()
-            Pkg.test()  # resolver may fail with test time deps 
+            Pkg.test("${{ matrix.package.name }}")  # 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
diff --git a/Project.toml b/Project.toml
index 7b39331..283ed65 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesTestUtils"
 uuid = "cdddcdb0-9152-4a09-a978-84456f9df70a"
-version = "1.13.1"
+version = "1.13.2"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
@@ -12,7 +12,7 @@ Suppressor = "fd094767-a336-5f1f-9728-57cf17d0bbfb"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
-ChainRulesCore = "1.11.2"
+ChainRulesCore = "1.11.2, 2"
 Compat = "3, 4"
 FiniteDifferences = "0.12.12"
 MetaTesting = "0.1"