Resolving template parameters

Hi,

I am looking for a way to achieve the following. I've tried a couple
of things, but they all ended up being too complicated:

I have a templated class A. I want another class B to be able to call
a method defined in A's base class which at runtime determines the
template parameters (I know ahead what is allowed) and calls a
templated member function B with A's template parameters.

I'm imagining something like this - I know that it can't work like
this, but I would like to achieve a similarly simple syntax:

class Base
{
public:
  virtual void call(...) = 0;
}

template <class T1,class T2>
class A : public Base
{
  public:
    void call(...)
    {
      if (typeid(T1) == ...)
        ...
      else if (...)
        ...
      else if (...)
        ...
    }
}

class B
{
public:

  void x()
  {
    Base *pSomePtr = ...;
    pSomePtr->call(this,&B::y);
  };

  template <class T1,class T2>
  void y()
  {
    // do stuff
  };
};

Any help on how I could realize this would be greatly appreciated .

Thanks,
Stefan