Be sure with MOC applications that you follow instructions. If they say to send 3 Letters of Rec, do NOT send more unless you are sure they will accept more. Each MOC has different policies and you need to check with each. Not following instructions is an easy way to get your extra letters tossed (which really isn't fair to those who spent time writing them) or, worse, getting your application tossed.
In terms of SAs, I can only speak for USNA which does accept additional letters of rec. However, they are NOT required. Also, if they don't add something that is not otherwise in your packet, don't bother. With letters from your math and English teachers, your activities list, your essay, and a BGO interview, most important stuff will already be covered. Remember, most SAs receive about 12,000 applications each year. Extra letters that don't add anything substantive are mostly a nuisance.