So so much support for this idea! <3
At least once a week, I get a trade, and half the time I have to edit due to this kind of problem.
It's just not fun, but adding something like this would definitely help make trading more fun in my opinion. c:
Like some other people have said, sometimes I just don't want to trade for hoards (happens very rarely mind you), and as for missed pets, I'm not in a rush to get them. People can't really tell WHY a pet is on your wishlist unless they carefully go through your groups (that is, if they're unlocked, otherwise it gets even more difficult and time wasting) or your 'trade rules/settings' and even then they can miss stuff.
It's not the other trader's fault that they can't tell the difference between hoards, missed outcomes, dreamies, etcetera. Since everything has to be lumped together in the one big wishlist. :c
This is a problem I see constantly, and I believe adding something like this suggestion of Shiro Tora's will be a big step forward in getting problems with trading solved.

EDIT: Another point is people that do art for pets, might have pets on their wishlist specifically for that, and they're not interested in trading pets for those, just want to trade art. If this customizable multiple wishlist comes about, this would be really helpful for artists that trade pets for art in separating pets they'd accept for commissions and pets on their wishlist for normal trades.