USNA will accept additional letters of recommendation beyond what's asked for. However, they stress that the additional letter(s) should show something about you that is otherwise not known to the Admissions Board.
For example, if you work after school and every summer for two years, you might get a letter from your employer. The reason is that you might have fewer sports/ECAs than someone not working and your employer can talk about you outside of school in a way your teachers, etc. can't. However, if you only worked at your place of employment for one month of one summer -- a letter from your employer probably won't do anything for you.
Another example -- if 90% of your ECAs are church-focused (or focused on some activity not associated with your school) and you've been involved in this activity throughout h.s. such that you have very few school activities -- a letter from the head of that activity might be beneficial.
What you do not want to do is compile a huge stack of letters each saying you are the nicest, most decent, hardworking person who wants USNA really, really badly. Not going to help. You don't want a letter from an admiral who barely knows you or letters from 10 USNA grads who know your parents and know that any kid of theirs must be great. Not going to help.
Most people who gain appointments provide what is asked and no more. You will not be disadvantaged if you provide only what's requested. It is rare for an additional letter of rec to have any influence unless, as discussed above, it brings out an important part of your life about which USNA would otherwise be clueless.