Do you even know what you're talking about before you post? Perhaps you should have your parents proofread your posts or even educate yourself a tad bit before hitting submit. As a level 12 Dead Orbit, level 10 Vanguard, and a minimum level 8 on the other 2 factions... I think I'm far more knowledgeable about rank up rewards with factions... and wouldn't waste my time asking the question. Eris currently has a max rank of 4. That's it. Once you hit 4, you gain no more experience towards her, therefore that's all there is to "ranking up" Eris. Because you cannot rank up any higher, there is only one opportunity for that emblem. And before any other idiot asks... yes I had at least 3 open spaces for emblems before reaching rank 4.

Eris isn't a 'normal' faction, though. You don't get any more rep from her bounties once you get her to 4, so you won't have another opportunity to get the emblem.