I haven't looked at the specifics in a while, but an elite monster is the equivalent of 2 monsters of the same CR. To do that it needs, roughly, 2x hit points and way to recover from conditions and negative effects when it is bloodied. The elite recovery is the method most often employed, but you could do it with a blanket recovery. However, you shouldn't be increasing DPR with this method. Also, though it is not part of the Elite Recovery ability, it really should have a method to recharge any traits or abilities.
Of course it can get more nuanced as seen in the "official" Mythic Monsters that elite monsters are emulating. So you could increase HP by 50% and then increase DPR by 50% (or there about) once it is bloodied. The are fun things you can do it you break out of the "template" mind set. Just think of it as two monsters of the same CR with a recovery mechanic when it is bloodied and your good to go.