Below is a valid enum declaration.
public enum SomeEnumClass {
ONE(1), TWO(2), THREE(3);
private int someInt;
public SomeEnumClass(int someInt
No, you can't; enum types all extend Enum, and they're implicitly final. Enums can implement interfaces, or you can declare the relevant methods directly on the enum class in question.
(I do see the basic idea of what you want, which is a mixin; perhaps the Java 8 interfaces will be a bit more useful in this regard.)