Is it possible for a world to have a common area but then an instanced sublevel?

I'd like to build a world where you start in a common hub, but you can go through some kind of portal to your own instanced area that is persistent--the state of it is saved from session to session. You can also invite friends to this private instance, but only you can enter it first. Everyone else needs to be invited or part of your party.

Imagine, say, an RPG where there is a town, but you can enter your own house and that house has decorations and items placed in it as they were when you left it.

Is this at all possible? Maybe a door that goes to a world which has a max of 1 player, and the state of the world is saved in player variables? But in that case you can't invite others to your world.