In general, I found the idea on
epic levels hard to apply to 5e.
In previous editions, you could just extend everyone's progressions beyond level 20, let's call it a "vertical epic" progression. IMHO it is always a very boring idea, not providing any fundamental epicness in the game. In 5e it might be more tricky to pursue, partly because of bounded accuracy and partly because there even aren't clearly linear progressions of abilities, and instead there are even some which "top" before 20. But if you really want "vertical epic", then presumably you can grant 10th+ level spell slots, and let characters cast augmented versions of regular spells.
The dual option is "horizontal epic", i.e. the regular character's progression stops at 20th, and after that the DM grants add-ons taken from the same options already available: more feats, more known spells or options, more magic items... It's easier to manage for the DM and doesn't tip the balance, but it still increases complexity for the players. There are no epic spells with this option.
The third way, which is the most interesting one, would be to indeed introduce something
different to what the PCs can do, but it is very challenging to design, but at least this is the kind of way that I would expect
epic spells to work.
From an epic spell I would expect it to be a gamechanger. Perhaps I would look
outside of combat for designing such spells, because in combat there are already spells that can work as insta-win. If you can
power word kill a BBEG before level 20, there is nothing more a spell can do in combat. You can remove some limitations here, increase the chance of success there, maybe make it work on multiple enemies... it will not change the fact that the spell already makes combat potentially won with no effort. Make it even more effective, and you've eliminated combat as an interesting part of the game.
But as for out-combat-spells, I can't think of anything better than scaling
duration,
area of effect or
number of targets tenfold, which isn't extraordinary interesting, but that's the main thing I think about at the term "epic spell". So instead of charming a bunch of people, you'd charm a whole nation. Instead of changing a plot of terrain, you'd change half a continent. Instead of enchanting something for a day, it would last for 1000 years.
The only spell that ever smelled epic to me in D&D was
Genesis in 3ed, which let a Cleric create a whole demiplane. But IIRC it has impossible costs to be used to really create another world, and it was then practically limited to being just a bigger
Rope Trick.
Something that changes
time would definitely feel epic, but good luck handling the consequential paradoxes then...
