diff --git a/src/subtype.c b/src/subtype.c
index 92140944a9aed..4c4244351b5d1 100644
--- a/src/subtype.c
+++ b/src/subtype.c
@@ -2803,6 +2803,14 @@ static jl_value_t *intersect_types(jl_value_t *x, jl_value_t *y, int emptiness_o
     jl_stenv_t e;
     if (obviously_disjoint(x, y, 0))
         return jl_bottom_type;
+    if (jl_is_dispatch_tupletype(x) || jl_is_dispatch_tupletype(y)) {
+        if (jl_subtype(x, y))
+            return x;
+        else if (jl_subtype(y, x))
+            return y;
+        else
+            return jl_bottom_type;
+    }
     init_stenv(&e, NULL, 0);
     e.intersection = e.ignore_free = 1;
     e.emptiness_only = emptiness_only;
diff --git a/test/subtype.jl b/test/subtype.jl
index f8a7c87005edd..bb808ad63d746 100644
--- a/test/subtype.jl
+++ b/test/subtype.jl
@@ -1615,3 +1615,22 @@ end
     Tuple{Array{Tuple{Vararg{Int64,N}},N},Tuple{Vararg{Array{Int64,1},N}}} where N,
     Tuple{Array{Tuple{Int64},1}, Tuple},
     Tuple{Array{Tuple{Int64},1},Tuple{Array{Int64,1}}})
+
+# issue #32703
+struct Str{C} <: AbstractString
+end
+struct CSE{X}
+end
+const UTF16CSE = CSE{1}
+const UTF16Str = Str{UTF16CSE}
+const ASCIIStr = Str{CSE{2}}
+c32703(::Type{<:Str{UTF16CSE}}, str::AbstractString) = 42
+c32703(::Type{<:Str{C}}, str::Str{C}) where {C<:CSE} = str
+
+@testintersect(Tuple{Type{UTF16Str},ASCIIStr},
+               Tuple{Type{<:Str{C}}, Str{C}} where {C<:CSE},
+               Union{})
+@test c32703(UTF16Str, ASCIIStr()) == 42
+@test_broken typeintersect(Tuple{Vector{Vector{Float32}},Matrix,Matrix},
+                           Tuple{Vector{V},Matrix{Int},Matrix{S}} where {S, V<:AbstractVector{S}}) ==
+             Tuple{Array{Array{Float32,1},1},Array{Int,2},Array{Float32,2}}