Writing a subscript non-member function

I'm guessing this just isn't legal in C++, but I thought I'd ask, given a struct that I don't own:

struct foo {
    int x;
    int y;
    int z;
};

I want to write a non-member subscript operator for it:

int& operator [](foo& lhs, const std::size_t rhs) {
    switch(rhs) {
    case 0U:
        return lhs.x;
    case 1U:
        return lhs.y;
    case 2U:
        return lhs.z;
    default:
        return *(&(lhs.z) + rhs - 2U);
    }
}

I'm getting this error:

error: int& operator[](foo&, std::size_t) must be a nonstatic member function

struct foo {
    int x;
    int y;
    int z;

  int& operator [](const std::size_t rhs) & {
    switch(rhs) {
      case 0U:
        return this->x;
      case 1U:
        return this->y;
      case 2U:
        return this->z;
      default:
        return *(&(this->z) + rhs - 2U);
    }
  }
};

not all operators can be overloaded as free functions.

Not the standard, but clearly written over at cppreference, the operators [], =, -> and () must be non-static member functions.

If you can do wrap(f)[2] you can get it to work. But there is no way to get it to work strait on a foo instance.

template<class T>
struct index_wrap_t {
  T t;
  template<class Rhs>
  decltype(auto) operator[](Rhs&& rhs)& {
    return operator_index( *this, std::forward<Rhs>(rhs) );
  }
  template<class Rhs>
  decltype(auto) operator[](Rhs&& rhs)&& {
    return operator_index( std::move(*this), std::forward<Rhs>(rhs) );
  }
  template<class Rhs>
  decltype(auto) operator[](Rhs&& rhs) const& {
    return operator_index( *this, std::forward<Rhs>(rhs) );
  }
  template<class Rhs>
  decltype(auto) operator[](Rhs&& rhs) const&& {
    return operator_index( std::move(*this), std::forward<Rhs>(rhs) );
  }
};

template<class T>
index_wrap_t<T> index( T&& t ) { return {std::forward<T>(t)}; }

then you can do this:

int& operator_index( foo& lhs, std::size_t rhs ) {
  // your body goes here
}
foo f;
index(f)[1] = 2;

and it works.

index_wrap_t forwards [] to a free call to operator_index that does ADL.