Is it possible to overload a function to properly accept any template as template template parameter, up to N arguments?

I know it's impossible to have a single template template parameter that would accept any template.

But I thought it was possible with enough overloads:

template <template <typename...> typename> void foo() {}template <template <auto    ...> typename> void foo() {}// 2template <template <auto    , typename...> typename> void foo() {}template <template <typename, auto    ...> typename> void foo() {}// 3template <template <typename, auto    , typename...> typename> void foo() {}template <template <typename, typename, auto    ...> typename> void foo() {}template <template <auto    , auto    , typename...> typename> void foo() {}template <template <auto    , typename, auto    ...> typename> void foo() {}// ...// 5 (just a single function for the example)template <template <typename, typename, typename, typename, auto...> typename> void foo() {}// A test:#include <vector>#include <map>int main(){    foo<std::vector>();    foo<std::map>();}

But alas, this doesn't work. E.g. std::vector causes ambiguity between <typename...> and <typename, typename, auto...>.

Getting rid of ... parameter packs doesn't help, now std::vector is an ambiguity between <typename> and <typename, typename> (because its second parameter has a default argument).

Replacing every pack X... with X, X... (except on first two overloads) also doesn't help. It works with std::vector and std::map, but if I try passing template <int, typename...> struct A {}, it gets matched against the <auto, typename, typename...> overload, because that overload is then unable to pass just one template argument to A.

Is there a solution?