The LDS Church currently does not allow its members to have two living spouses. Anyone in the Church with more than one living spouse is most likely keeping it a secret from member friends and local leaders. Consequently most members take the Church's current position to mean that the Church doesn't practice polygamy and others might not believe its part of Mormon doctrine.
However, the fact is that polygamy, when divinely commanded, is a divine principle according to Mormon scripture, and God could at any moment bring it back.
Not that it's actually gone away completely. Currently apostle Dallin Oaks is expecting to live eternally with at least two women. He married Kristen McCain after his first wife, June Dixon, passed away. He is eternally sealed to both women, who get to share his eternal companionship.
Eternal companion #1
Previous wives don't have to be dead though. Today a Mormon man can be sealed to more than one living woman as long as he is only legally married to one and not cohabitating with the one(s) he had divorced. In other words, a man can be sealed in the temple, divorce that wife, and be sealed to another woman even if the first is still alive.
I'm not sure if the Church puts a cap on how many times a man can divorce and be sealed to a new woman, but I do know that there's a cap on how many times a woman can be sealed in the temple while living. Once. Any marriages following a death or divorce are for time only.
Yes, that's sexist. No, I don't think it's right.