It's not really feasible right now. So much of the client is built around there being two teams that it would take a massive effort to overhaul the system to support more than that. It's more resources than Riot really has to spare at the moment.
Besides, I'm not even sure how it would work when it comes to decreasing nexus health... does only the team with the fewest bases lose points? Any team not currently in the lead? What about when two teams have a standoff at controlling 2 points, while the 3rd only controls one, dragging the game on longer than Dominion should last?