Well, that is beside the point being made, but yes, players can and do sign exclusive contracts separate from their schools. Those funds do not go into a shared pool as Orange stated correctly.
Many of the highest profile players do enter into such contracts, but also witness Paige who has not for this particular NIL opportunity as her NIL merchandise seems to be available on the general site for her school, but I would surmise her cut is close to 100% there (and she does have many exclusive deals also) but that is pure thought speculation as far as the cut she gets on the team site, she may be a very generous type, I suspect she is.
Don’t think for a minute this is a dig on any player who chooses to go exclusive, and tbh, I would not blame them. The schools usually keep the number rights in most cases, but with Paige, who I respect a bunch and think a lot of, I would not be surprised if she is spreading the wealth to her teammates.
Like everything in life, the terms and conditions for every opportunity vary, and schools and players work together to maximize obviously.