For example, if Nagato use Ningendo and extract soul from someone, can that soul be used for reviving someone else?
A common misconception is that a life is needed for the Rinne Rebirth.Let me clear that first.
During Pain's fight with Naruto,when Pain becomes good,he uses the Rinne Rebirth to revive everyone he's killed.At that point,Konan tells him that he doesn't have enough chakra to cast such a powerful jutsu.
So you need a large amount of chakra to pull off the Rinne Rebirth-which is often confused with the life of a person.You could die because of the exhaustion though.
Now coming to your question.
Yes,it is possible if the life force of the person from whom you've pulled the soul out is enough for the jutsu to be cast.
Example:You can't expect a 5 year old boy's life force to be enough for the Rinne Rebirth.
not really, but the jutsu just retract enormous amount of chakra from once body which people dont normally survive because of the exhaustion after the jutsu has taken effect, one of the events this happened was when Naruto was battling the seven pain, his sibling nagato, konan but that was after Naruto defeated them. and went where the seven pains main chakra was generating