I remember seeing that Mearls said they nearly released 5e as a 1-10 level game. I think that would have been a good idea, they could have done a level 11-20 supplement later once they saw more of how the game worked.
That would be a fun experiment.
What if we retroactively applied 4e lessons to 11-20?
4e made 11-20 and 21-30 interesting by adding on a new mechanic -- paragon paths and epic destinies.
We could do the same!
In my case, however, I'd steal something different from 4e; the power source. And make it mechanical.
Power Source:
A mere mortal cannot pass level 10, no matter how hard they practice. In order to pass level 10, you need a
power source.
This power source is a narrative and mechanical feature. You can have more than one power source. Power sources add features, like classes or magic items do.
The sum of the levels of your power source are equal to your character level past 10.
Power sources often have optional features. Having access to spells above level 5 is a power source feature.
Many power sources require narrative justification. Power sources can, however, be latent: you can fullfill the requirements many levels before. In other cases, they can be hidden parts of your character's backstory with a DM agreement. "Dragon Blooded" can be unlocked if you killed a dragon at level 5, for example.
---
So Power Source replaces the Paragon Path. It also provides a great excuse why your town guardsman mercenary is now superhuman.
---
Then we can unlock Epic Destinies at level 17. It could have a 5 level progression - 17:1, 18:2, 19:3, 20:4, then getting epic level 5 requiring some deed or whatever.
So instead of level 20 fighter, you'd have:
Level 20 Fighter
Level 10 Dragonblood
Level 5 Returned Emperor