You should apply to all nominating sources where you qualify. Do not concern yourself with "taking someone else's nomination" or any thinking along those lines.
If you were to receive a Prez, and 3 MOC nominations you would not be considered for VP. The VP nominations are typically granted to highly qualified candidates who do not have a nom.
The more competitive the area, the more likely the MOCs share information so there is only one nom per candidate.
In our state, no one received a nom from both senators, but many received a second nom from their representative. In other states, all worked together and no one receieved more than one nom out of the 3 possible. And I recently heard some areas are so competitive that candidates must accept or decline their nom.
Remember, if you only receive ONE nomination, it is true that is all you need to get an appointment (and there are MANY cadets who only had one nom), but that does NOT mean you are guaranteed an appointment. One nom may make you one out of ten on a competitive MOC slate. If you do not "win" the slate, you may not get an appointment. The more noms you have, the better your chances of an appointment.