Typically, since we are working in java, and usually proscribe to OO design, you could get this functionality through extension. However, enums extend java.lang.Enum implicitly and therefore cannot extend another class.
This means extensibility for enums most be derived from a different source.
Joshua Bloch addesses this in Effective Java: Second Edition in item 34, when he presents a shared interface pattern for enums. Here is his example of the pattern:
public interface Operation {
double apply(double x, double y);
}
public enum BasicOperation implements Operation {
PLUS("+") {
public double apply(double x, double y) { return x + y; }
},
MINUS("-") {
public double apply(double x, double y) { return x - y; }
},
TIMES("*") {
public double apply(double x, double y) { return x * y; }
},
DIVIDE("/") {
public double apply(double x, double y) { return x / y; }
}
This is about as close as you can get to shared state when it comes to enums. As Johan Sjöberg said above, it might just be easiest to simply combine the enums into another enum.
Best of luck!