Now that there are a lot of games with avatar awards, it looks like Microsoft has limits they put on how many a game can award, just like achievements.  So far no retail game has more than 5 and no XBLA game has more than 2, and DLC looks limited to 2 also.  I'm counting each male/female set as one.  So even if it's 2 noticeably different items like from Red Dead Redemption, each avatar can only earn one of them.  In fact no XBLA game has anything other than 2, and the only retail games with less than 5 are Alan Wake and Lips.  Alam Wake might be a special case because it's only the collector's edition.  It might very well be that collector's editions get 1 or something.  Since there is only one so far, it's impossible to tell. 
 
Halo Waypoint is kind of an oddity since it has 8, but it's also not a game, and it only gives 5 from ODST.  These rules probably aren't a secret, just nobody over at MS seems interested in talking about avatar awards yet.  Maybe since almost ("I'm Castlevania, I'm better than you other games") every Summer of Arcade game this year has them, the awards will get a little press.