diff --git a/Project.toml b/Project.toml
index b213cc39d..1a1bbdb1b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "0.9.31"
+version = "0.9.32"
 
 [deps]
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
diff --git a/src/differentials/composite.jl b/src/differentials/composite.jl
index 36d21853e..10eb50730 100644
--- a/src/differentials/composite.jl
+++ b/src/differentials/composite.jl
@@ -180,6 +180,12 @@ canonicalize(comp::Composite{<:Tuple, <:Tuple}) = comp
 # Dict composite are always in their canonical form.
 canonicalize(comp::Composite{<:Any, <:AbstractDict}) = comp
 
+# Composites of unspecified primal types (indicated by specifying exactly `Any`)
+# all combinations of type-params are specified here to avoid ambiguities
+canonicalize(comp::Composite{Any, <:NamedTuple{L}}) where {L} = comp
+canonicalize(comp::Composite{Any, <:Tuple}) where {L} = comp
+canonicalize(comp::Composite{Any, <:AbstractDict}) where {L} = comp
+
 """
     _zeroed_backing(P)
 
diff --git a/test/differentials/composite.jl b/test/differentials/composite.jl
index 599c50b22..50dfddc0f 100644
--- a/test/differentials/composite.jl
+++ b/test/differentials/composite.jl
@@ -153,6 +153,16 @@ end
         @test canonicalize(CFoo(y=10)) == CFoo(x=Zero(), y=10)
 
         @test_throws ArgumentError canonicalize(CFoo(q=99.0, x=2.5))
+
+        @testset "unspecified primal type" begin
+            c1 = Composite{Any}(;a=1, b=2)
+            c2 = Composite{Any}(1, 2)
+            c3 = Composite{Any}(Dict(4 => 3))
+
+            @test c1 == canonicalize(c1)
+            @test c2 == canonicalize(c2)
+            @test c3 == canonicalize(c3)
+        end
     end
 
     @testset "+ with other composites" begin