To the Addy's implementation I just added a fake constructor in order to prevent misuses of the singleton pattern. As you can see, the Singleton pattern purpose is to ensure there will always be only one instance of it's "class".
After reading it I wondered if there could be a way to make singletons inherence possible. I finally got it by adding a simple snippet to the previous implementation:
As you can see our singleton inherits from the parent constructor we have given it. It also can take a conventional objet constructor or another singleton.
The main use case for it is the ability to extend to another conventional constructor the singleton pattern. It also provide a way to extend existing singletons and change their behavior with no risk to alter them.