Historically, USNA has accepted additional letters of rec but, unless they meet certain parameters, they are useless.
They are helpful if they cover a part of your life that cannot be covered by your teachers or BGO or by the other information you submit. Some examples . . .
You must work during the school year (e.g., to support your family) and thus don't participate in sports/ECAs -- a letter from your employer would be helpful. This does NOT apply to those who work summer jobs or work a few hours per week during the school year.
All of your ECAs are outside of school -- e.g., your church. Here, a letter from your religious leader might be helpful to describe what you do. This does NOT apply to someone who is very active in school and also in scouting or some other ECA outside of school.
Things that really don't help -- family friendd (including military officers and politicians) who say you are a great human being who would be a great mid/officer. Additional letters from teachers, club advisors, employers, friends, relatives or others who will simply reiterate the comments of your Engllish/mah teachers don't help at all -- and won't overcome weak recs from these mandatory recommenders.
USNA receives tens of thousands of applications. If each candidate submitted only one extra rec, that would mean 10,000+ recs to read. In the overwhelming majority of cases, they will not help at all. You might check with your BGO regarding your specific circumstances.