I've never actually experienced or seen a server transfer happen myself. This is just to confirm the rumors that it actually did exist at one point, at least in KR, for individual characters.
Quote from Slayerj;1277067:
Couldn't we keep the ability to play as pets (though no one really does that anymore) via having the pets labeled or something using the players account/character names, or something?
That's a system mabi doesn't have.
Anything to handle any of this, mabi doesn't have. All of it would need to be designed, structured, coded, and edited into the existing game from scratch. A rename system, a sub-character system, a pet ID system, a post-move tagging system, how to handle server-centric data, all of it.
Mabi has nothing to handle any of it, all of it would need to be created first. And given the state of accounts and things in mabi, that's unlikely to happen barring an account system rewrite.