Class Template specialization for multiple types

I found a few questions that ask something similar but could not find a straight answer for my particular case. The whole syntax for Templates is very confusing to me so I may just misunderstood something.

I have a class template that is supposed to accept every type. Simple example:

template <class T>
class State {
  public:
    void set(T newState);
    T get();
  private:
    T state;
};

template <class T>
void State<T>::set(T newState){
  state = newState;
}

template <class T>
T State<T>::get(){
  return state;
}

Now I would like to have a specialised template for a group of types that adds an additional function for these types. From what I found out so far I can utilize so called type_traits but how exactly they are used to achieve this is still a mystery to me.

F.e. this specialization for the int type but instead of writing this just for the int type I would also like to allow all other int and float variants. I found std::is_arithmetic but have no Idea how to utilize it to achieve this.

template <>
class State <int> {
  public:
    void set(int newState);
    int get();
    int multiplyState(int n);
  private:
    int state;
};

void State<int>::set(int newState){
  state = newState;
}

int State<int>::get(){
  return state;
}

int State<int>::multiplyState(int n){
  return state*n;
}