Why is it not possible to overload class templates?

Question

Reading this question made me wonder: is there a technical reason for disallowing class templates overloads?

By overloading, I mean having several templates with the

Answer 1

You cannot "overload" type parameter, non-type argument and template template parameter, but you can specialize variadic template:

template 
struct Foo;

template 
struct Foo {};

template 
struct Foo {};