I'm not sure if USNA takes the same approach for enlisted personnel as it does for non-military applicants.
For the non-military types, USNA primarily focuses on the 3 required recs (two teachers and your BGO). They will consider up to two (I believe) additional LORs but those are unlikely to have any impact unless they shed light on some part of your life that is not covered by your teacher and/or BGO recs. If you search this forum you'll find several discussions on this point.
USNA reviews thousands of records each year. If each of 10,000 applicants all submitted even 2 extra letters . . . well, you can do the math. Submitting multiple LORs won't help your application and is likely to dull the effect of one very significant extra LOR.
As noted, I don't know if this applies equally to prior enlisted. I suspect that it does but can't say for sure. I would think the required letter(s) from your command would carry the most weight.
