Post Praetorian said:

Simply start a new franchise. Call it something new. Call it Nevada Jones if it must ape its predecessor, but do not force us to pretend to pretend.

Or give the franchise an overarching title like "You Call This Archaeology?" (that was a joke, you know what I mean), and have the Indiana Jones movies be the story of one character. The new movies could be based on someone completely different, just living in the same universe, perhaps even in the same time as Mr Jones.