First, I'll defer to your son's BGO regarding his particular situation. It may make sense, for various reasons, for him to submit add'l letters of rec.
However, as a general rule, consider carefully whether you want/need to do so. There is a theory that extra letters can't hurt. However, they may not help. USNA gets about 17,000 applications per year. Let's assume that 7,000 of those submit letters of rec. If each of those submitted 3 extra (in addition to the 3 that are required), that's 21,000 more letters for USNA to read. Thus, if yours doesn't really stand out in what it says (not necessarily how it's written), it isn't likely to get much notice.
The admissions decision will largely be made on the basis of objective facts -- grades, classes taken, class rank, CFA scores, etc. Teacher recs are important. BGO recs help round out the candidate in that they cover different topics. There is a personal essay where you can include things that might not otherwise be obvious.
So, after all of this, ask yourself, "What else about me is REALLY important for USNA to know and who would be the best person to address that?" The fact you're a really great guy/gal who is super active in sports and school activities, etc. is probably already covered. However, if there is something that isn't covered, then you might want a letter that discusses this.
What are some possible examples: you work 20+ hours per week during the school year and full-time during summer; you are the top person in the state in judo; you are very active in the State Fair; 95% of your activities are church-related, etc. In these cases, a letter from your employer, minister, coach, etc. might add something about a critical aspect of your life.
As noted above, the letter must say something about you that will get you noticed. Sort of an "I didn't know THAT (in a good way) about him/her." That is where add'l letters can really help.