The short answer is "Well, it depends. How bad do you want to attend USNA?"
Yes, it is possible to have multiple nominations. Yes, pursue all sources. If you received a Presidential for example, those are given to all who apply and qualify, non competitively. There are more given than there are appointment slots available. Everyone with a presidential does not get appointed with that nom source. If that's your only nomination, the ship may well sail without you on deck.
The more noms you have, the more flexibility the academy has in getting you an appointment.
Apply for all you can and put together the very best package for each application you possibly can. Applications for nominations should receive as much of your attention as your application to USNA!