Hmmm. Maybe make use of the Wild Magic table. Allow a Sorcerer to replace a spell between levels, but the new spell gets Wild Magic results for a couple days.
I admit this is a matter of personal taste, but I HATE the very concept of limited spells known. Detest it, and detest classes that are built that way. Every class has a big, beautiful spell list (some more than others, but that's neither here nor there), and a player of a limited-spells-known class will never get to use most of them. It's a waste. It also limits my (as a DM) flexibility, because I can't count on the characters having access to any particular magic when I make my adventures.
So.
I have made house rules that allow for some flexibility in the classes that don't have it per the PHB. Bards have a "song book" that mostly works like a Wizard spellbook (except it's written in a idiosyncratic musical notation, get it?), and they prepare spells with daily music practice. Warlocks can "borrow" 2-3 spells (in addition to their regular Spells Known) from their patron at the end of a long rest, and can cast them using a regular spell slot or Mystic Arcanum slot.
But what about Sorcerers? I'm struggling to think of a house rule that would allow for some flexibility while being consistent with the classes' concept of a natural, intuitive spellcaster. Any ideas? Has anyone implemented a similar rule?
(Please no replies of "Don't do this" or "That isn't what the Sorcerer is". I don't care. I'd rather just nix the class entirely than have a class with limited spells known. Solutions only, please. Thanks.)
oh! oh! oh! mr kotter mr kotter. you forgot after the 45 seconds. The dm gets to taser the player.Here is my suggestion.
The sorcerer can cast any spell off the sorcerer list. However, the sorcerer has 45 second wall clock time to complete their turn, otherwise the spell fails. Bonus action spells have 30 seconds, reaction spells 15 seconds.
This gives enormous flexibility to the sorcerer, while not reintroducing the main problem that spells known prevents.
Oh, and the sorcerer needs to give up something for the increase in power due to the extra flexibility. This is not a joke. Seriously, casters are already at absolute worst at par with non-casters - if you give something more to casters, you must take something away from them as well otherwise they will dominate non-casters, especially at higher levels.

(Dungeons & Dragons)
Rulebook featuring "high magic" options, including a host of new spells.