Extending a enum in Java

You can implement a common interface

interface I { }

enum A implements I {
   A, B
}
enum B implements I {
   C
}
public void functionA(I i) {
    //do something
}

obj.functionA(A.A);
obj.functionA(B.C);

You can't.

Enum types are final by design.

The reason is that each enum type should have only the elements declared in the enum (as we can use them in a switch statement, for example), and this is not possible if you allow extending the type.

You might do something like this:

public interface MyInterface {
    // add all methods needed here
}

public enum A implements MyInterface {
    A, B;
    // implement the methods of MyInterface
}

public enum B implements MyInterface {
    C;
    // implement the methods of MyInterface
}

Note that it is not possible to do a switch with this interface, then. (Or in general have a switch with an object which could come from more than one enum).