Overload variadic template's fixed parameters

Is it possible to override a variadic template by changing the number of fixed parameters before the function parameter pack? For example:

#include <iostream>

template <typename ...Args>
void foo(std::string, std::string, std::string, Args...) 
{ 
  std::cout << "THREE STRINGS\n"; 
}

template <typename ...Args>
void foo(std::string, std::string, Args...) 
{ 
  std::cout << "TWO STRINGS\n"; 
}

int main() {
  foo("key", "msg", "data", 1, 2);
}

Running this causes the second foo to be called, but I want the first to be called. Is there a better way to overload this function?