diff --git a/.github/workflows/downstream.yml b/.github/workflows/downstream.yml
index 3da495f..019143d 100644
--- a/.github/workflows/downstream.yml
+++ b/.github/workflows/downstream.yml
@@ -62,7 +62,7 @@ jobs:
             # 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
+            Pkg.test(test_args=["--downstream_integration_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
diff --git a/test/runtests.jl b/test/runtests.jl
index eda9b89..55d00f1 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -6,8 +6,10 @@ import BandedMatrices: _BandedMatrix, BandedColumns
 import Base.Broadcast: broadcasted, Broadcasted, instantiate
 
 using Aqua
+downstream_test = "--downstream_integration_test" in ARGS
 @testset "Project quality" begin
-    Aqua.test_all(InfiniteArrays, ambiguities=false, piracies=false)
+    Aqua.test_all(InfiniteArrays, ambiguities=false, piracies=false,
+        stale_deps=!downstream_test)
 end
 
 @testset "construction" begin