Well, by the time we got to Season Three of Star Trek
, Scottie had sort of made the move to a big enough status as to almost make it a "Big 4." I don't see why a "Big 4" couldn't happen in the films, though with Uhura this time.
Though, the new film is much more like the first season of Star Trek
, where it was much more of a "Big 2." McCoy is certainly important in the first season, but he becomes much more vital as the show goes on.