It’s been a while since I read LOTR, but I think it was clearly established that someone on the level of Gandalf or Galadriel (like Sauraman) got their hands on the One Ring, they could control it rather than have the ring threaten to overpower them and/or turn them into a monster. Sauraman certainly believed this to be true – he wouldn’t have gone to so much effort to take the ring if he didn’t think he could use it. (If he couldn’t, destroying it was clearly the wise choice even if one wants to rule in Sauron’s place.)
Gandalf does not have a major power base, which is clearly required as both Sauron and Sauraman built up massive armies, but Evil Gandalf can presumably change that by turning the humans and dwarfs into his servants, either through proxies or simply using his earlier reputation to convince them to support him. (Twist – if this starts early enough, he might get his hands on Smarg too). If he does, and if he can use the ring, he might overthrow Sauron and then go on to impose his own order. Or he might face challenges from Sauraman (who will guess the truth) and Galadriel, sparking off a war that will weaken the forces of good while allowing Sauron to build up his own armies and crush the winner.
Galadriel (and Sauraman) do have power bases, so if they get the ring and become evil – Sauraman is already 9/10s there – they will pose a more immediate threat. In this world, it may take some time for Gandalf to realise what’s happened (depending on how it plays out), giving them time to take full power and use the ring. Again, we wind up with a civil war – ironically, this time Sauraman and Gandalf may wind up on the same side, both fighting to stop Evil Galadriel and the former, at least, also planning to take the ring himself afterwards.
There was a fan fiction about something like this -
https://www.fanfiction.net/s/2232043/1/Love-Me-and-Despair
Of course, if they’re wrong and using the ring gives Sauron access to the bearer’s mind, they’re going to be warding off his influence (like Frodo) or completely overwhelmed. In this world, there will be no war between Sauron and Sauraman. They’ll be on the same side.
Chris