Extend anonymous union in template specialization class c++

Let us suggest I have a class called vec4. Its a template and could be uint8, float or int in most cases. Other cases are allowed but are less likely. The class looks like this:

template<class T>
class vec4 {
public:
    vec4(){}
    virtual ~vec4(){}

    union {
      struct {
        T x,y,z,w;
      };
      struct {
        T r,g,b,a;
      };
    };
};

This helps me think about a problem in different ways when writing code and allows me to do other cool things also and I rather enjoy the design pattern when ever applicable.

The problem is I would like to extend the class and add functions in the case it is a 32 bit float. That I can do. I would also like to extend the union for a further maths paradigm where the third members are T c,y,m,k.

I am finding it very difficult to find material on the subject.