How do I extend a protected method in X++?

Protected methods can be wrapped with Chain of Command when the method is wrappable.

[ExtensionOf(classStr(MyClass))]
final class MyClass_Extension
{
    protected void processInternal()
    {
        next processInternal();

        // Additional logic.
    }
}

Extension classes can also access protected members of the augmented class.

Private members are still private. CoC does not magically make them accessible.