A small signpost towards levels 21+ can be found in the capstone abilities of several classes with key powers that refresh after a short or long rest: "If you roll initiative and have no inspiration/mastery dice/sorcery points left, then you gain one X."
So in 5E, I think part of being epic will mean you get to use your class features more frequently. I can easily imagine epic-level characters gradually increasing this sort of minimum reserve. For other classes, we can see more channel divinity, more arcane recovery, etc. The point being that these characters stay at the top of their form longer, and can get through more encounters.
I can also see the proficiency bonus and ability score increases continuing up to L30, just as they do with monsters. Something would have to be done about the PCs' weak saving throws, however.
Ben