enable MANY class's member fields at once, depending on template <T>

Question

Here is MCVE. It works :-

template<bool c3> class Has3 { };
template<> class Has3<true> { public: int cat3; };

template<bool c2,bool c3> class Has2 : public Has3<c3>{ };
template<bool c3> struct Has2<true,c3> : public Has3<c3>{ public: int dog2; };

template<bool c1,bool c2,bool c3> class Has1 : public Has2<c2,c3>{ };
template<bool c2,bool c3> struct Has1<true,c2,c3> : 
     public Has2<c2,c3>{public:  int rat1; }; //<- ugly, in my opinion.

int main(){
    Has1<false,true,false> h; 
    h.dog2=5;
    //h.cat3=4;  //<- compile error (which is good)
}

The above inelegant MCVE is modified from enable class's member depending on template, which can enable only one field at a time.
(I read both answers, but its second solution uses too much memory.)

How to toggle many fields on/off easily?
It is sad that this MCVE becomes a mess pretty fast.

In my real cases, I have about 5-6 unique fields, that are different types.
For simplicity, the type of cat3,dog2,... does not depend on T.

Answer 1

You might have something simpler with:

class Cat  { public: int cat3; };
struct Dog { public: int dog2; };
struct Rat { public: int rat1; };

template <typename... Bases>
class Group : public Bases... {};

And then

Group<Dog, Rat> h;

h.dog2=5;