My son applied to USMA, USNA, and USAFA. Each of the three MOC's he applied with asked him to list his preference in order. On each he listed USMA first. Our Congressman ended up giving him a nomination for each academy, which took pressure off. The First senator gave him a nom for USMA only. Therefore, having two USMA noms in hand, at his interview with the second Senator, he asked the committee if he could change his preferences, and they allowed him to do so. To an extent you can game the system a bit.
Some will suggest you shouldn't get greedy, and that you should allow others the chance to get their nomination once you have one. This is hogwash though. It is a very competitive process, and you should maximize your personal chance for an appointment. The more nominations you have the better your odds of appointment.