None. (Well, maybe if you're a recruited athlete for football). In all seriousness, USNA doesn't care whether you've applied to other SAs and may not even realize you have. The fact that you are offered appointments to other SAs doesn't even matter -- it's not uncommon for folks to get offers to another SA and not get one to USNA (and I'm sure the converse is also true).
You definitely should not apply and absolutely should not attend a SA if your heart isn't in being there and/or you have little interest in a career in that service. The reason? Your chances of not succeeding (of quitting, failing, etc.) go up exponentially. A SA is tough enough when you're 100% committed on day one. If your heart isn't entirely in it, it will not be a good experience.
If your desire is to attend one SA, put 100% of your effort into securing that appointment. Only those who would be truly happy at a second SA should apply to more than one.