USNA doesn't "encourage" any more than the two required LORs. As noted, they will accept others; however, as OSDAD said, they need to say something "new."
LORs that are usually NOT helpful include those from: long-time family friends, other teachers, h.s. coaches (as a general rule), military officers you happen to know, summer employers, etc.
Those that MIGHT -- and I really emphasize MIGHT -- be helpful are the following:
-- Employer IF you work durig the school year (often to support your family) such that you really can't participate in school actitivies
-- Non-h.s. ECA or sports leader (e.g., religious leader, Scout leader, non-h.s. coach) IF this is your primary or only ECA/sport and thus your h.s. teachers are unable to comment about it.
There may be other examples but, as you can see, extra LORs should be the exception, not the rule. USNA expects that the LORs they request are sufficient to give the information they need (along with the rest of your packet). With the thousands of applications they receive, additional LORs only add work to the process. Thus, if it doesn't shed "new" light on the candidate, it's not going to carry any weight and was just a waste of time for the writer and reader.