These things live outside of time. Every time a universe is overwritten while one of these ships are outside time, are bound to meet temporal doppelgängers born fresh from the new universe they're moored to. They never know what's going to spring up out of "now" beneath them, whether it be complete assholes or mirror copies who will sign up not quite aware that it's probably relative minutes till their reality is superseded by yet some new mockery of what was. Dozens or hundreds, or thousands of Relativitys staffed by Braxton, Ducane and...
Unless planets, maybe solar systems or even a galaxy or two are completely temporally shielded and immune tot he buggering about by time experimentations by oddjobs elsewhere that crosstime there is only one Earth and one Federation.