Specialize template class constructor on templated template parameter

I am trying to find a way to deal with some legacy code. There is a templated class which I would like to specialize the constructor to pass different arguments to its base when instantiated with a certain parameter.

template<typename T, typename U>
class A : public U {
public:
    A(T &t, bool b);
    // Other member functions
}

template<typename T, typename U>
A<T, U>::A(T &t, bool b) 
    : U(t, b) {}

I need to change thebehavior of this constructor when U is of a certain (templated) class.

template<typename Z>
class S;

template<typename T>
template<typename Z>
A<T, S<Z>>::A(T &t, bool b)
    : S<Z>(t, b, false) {}

Is this possible? I know that class template specializations cannot be done without redefining a new class. But I would rather only specialize this behavior, and not any other member functions of this class U.