c++ templates more than one prototype

I have a relatively complex template with a lot of arguments (most of them with default values). For example:

template <typename I,
          typename S = BasicS<I>,
          typename C = BasicC<I>,
          typename E = BasicE<I> >
class Foo ...

Unfortunately whatever order of the arguments I choose there are always cases where you may want to change only the last one.

How I could create more prototypes for the same template, say

template <typename I,
          typename E>
class Foo1 : Foo<I, BasicS<I>, BasicC<I>, E >
{
    ... redefine the constructors
};

but without inheritance to avoid the need of redefining the constructors