You can’t specialize a member function without explicitly specializing the containing class.
What you can do however is forward calls to a member function of a partially specialized type:
template<class T, class Tag>
struct helper {
static void f(T);
};
template<class T>
struct helper<T, tag1> {
static void f(T) {}
};
template<class T>
struct C {
// ...
template<class Tag>
void foo(T t) {
helper<T, Tag>::f(t);
}
};