I think "House" should end with him and his team being replaced by a computer. It will need to be a robot (like the one on Lost in Space, ideally), not a web page, but symcat has the right idea. It would also be cool if the robot was a master game-player, finally putting House in his place.
You do know this is the final season of House? Would you rather see them continue to turn Chase into a Mini Me version of House (getting scruffy, painful injury, ignoring protocol) or witness a battle for relevance against a robot with smarts like the Watson computer? I'll take the robot battle.