My main beef with calling yourself a Unicorn is that I don't think it's a very nice thing to be.
Unicorn Hunters are usually a married couple who have decided that the best way to ease into Poly is to find a Hot Bi Babe who will fall in love with both of them equally, have hot threesome sex, help with babysitting and pretend she's just a friend when anyone's looking. The hunters usually have a laundry list of requirements their prey must match but no intention of changing anything about themselves in order to ensure their "new addition" has her needs met too. They usually blunder around with all the tact of baboons in heat before declaring themselves astonished that nobody is throwing herself at them on the basis of a two-line personal ad which states nothing more than their location and the fact that they want to add to their family. I've not encountered people looking for a male unicorn, possibly because the people who Unicorn Hunt also seem to be people who find bisexuality in men icky.
There are, of course, couples who successfully integrate one or more extra people into their relationship, but the way they go about doing so is what differentiates them from Unicorn Hunters and is what makes the additional partners partners rather than Unicorns.