I think of an egalitarian approach in terms of behavior. Of course you may not have the depth of feeling for someone you are just getting to know as you would a long time partner, but once you have decided to pursue a relationship with a new person, it means s/he deserves the same consideration as the long-time partner - just as we manage with our non-sexual friends. I don't use a hierarchy with them. I don't value one friend more than another - they all give me something different. So why would I use a hierarchy with lovers?
That new love is a human being with real live feelings; not a play thing that can be ignored on a whim.