I want to have a Class object, but I want to force whatever class it represents to extend class A and also class B. I can do
Java does not have multiple inheritance as a design decision, but you may implement multiple interfaces.
As of Java 8 these interfaces may have implementations.
To use multiple classes there are other patterns:
If the parent classes are purely intended for that child class, but handle entirely different aspects, and were therefore separated, place them in a single artificial hierarchy. I admit to doing this once.
Use delegation; duplicate the API and delegate.
Use a lookup/discovery mechanism for very dynamic behaviour.
public T lookup(Class klazz);
This would need an API change, but uncouples classes, and is dynamic.