As the tin says. Alexander of Battenberg remains as Sovereign Prince of Bulgaria (maybe even upgrading his title to king later), rather than abdicating and leaving. Obviously this might necessitate better relations with Russia (AIUI the Russians played a large part in him being removed, they essentially wanted a puppet ruler to kowtow to St. Petersburg, hence why they were willing to support Alexander, being nephew of the empress, but their first choice had been an Oldenburgski prince), although I'm not sure why necessarily, Ferdinand of Coburg-Kohary married a Catholic wife, and didn't really bow and scrape to Russia the same way they expected Alexander to AFAIK.
I'd imagine that Alexander marrying Victoria of Prussia might help in this regard, since then Russia would have to watch out for Britain AND Prussia if they were to try any funny business like OTL.