I'm not aware of any alternative email protocol that's implemented, except TMTP. I don't believe closed-source, walled-garden services, which don't allow third-party clients or servers, really count as legitimate alternatives.
There's Matrix, but that's a synchronization protocol for chatrooms, not a store-and-forward messaging scheme.
https://en.wikipedia.org/wiki/Dark_Mail_Alliance
The stuff Ladar Levinson created after the Lavabit takedown, (famed for begin Snowden's email provider). Although I'm not just talking about email protocols; but additions or other improvements that always have the same problems (PGP encrypted email, or whatever Facebook tried to do when they reinvented email...)