However, by applying for more than one, it certainly DOES increase your chances of getting accepted into one of them.
But may decrease the odds of your getting into your first choice SA -- especially if you're in a competitive district/state. Here's how it works. Let's say, hypothetically, that USNA is your first choice, USMA second, and USAFA third. You apply to all 3. Your MOCs ask you to choose or to rank your SAs. Let's say you choose USNA for one MOC, USAFA for the second, and USMA for the third. You only get a nom to USAFA. Guess where you're headed?
It's not a question of the SAs, it's a question of getting the nom. That's why I say, if you'd be perfectly happy at more than one SA, you may want to "split" your noms. If you have a preference -- especially a strong preference -- you should put all of your eggs in one basket.
Two caveats . . . this obviously doesn't apply to USCGA because it doesn't require noms. Also, if you live in a less competitive state/district, your MOC may give you noms to multiple SAs and this definitely increases your chances of getting into one.
It is my understanding from my DS interview process that they will ask you if you would be willing to accept an appointment to any other SA. His reply was" No i am only interested in USNA". Did that help who is to know did it hurt I would say no -it shows you have researched all of the academies and know the path you plan to take.
It doesn't necessarily help or hurt. Per my comments above, the MOC may have more candidates than slots for one SA or may have an imbalance of applicants for one SA. So you could be in a situation where the MOC would give you a nom to SA#2 (your second choice) but not SA#1 (your first choice). In this case, saying "no" on SA#2 may mean you'll get no nom. Or, it could be that the MOC is just testing the waters, so to speak. The MOC may have a number of folks who only want SA#1. If you'd be happy with SA#2, the MOC may give you that nom, so more people are happy. Or, it may be that, if you say you'll only take SA#1, the MOC will give you that nom because you're super competitive.
As you can see, it's a crazy system and, in most cases, you won't know what the MOC (well, his/her nom committee) is thinking when you're asked the question. They really don't care what decision you've made (one SA or happy at >1). They're simply trying to fill too few slots with too many applicants and trying to make as many as possible as happy as possible. Which . . .
Brings me back to the advice above. IF you would be truly happy (NO regrets) at more than one SA, then say so. If you have a preference, then go with that. The worst thing is to end up at a SA that you don't really want to attend -- I've had that happen to candidates in the past and it really didn't go well.