The reason we wanted to get a second dog is because Loki spends a lot of time alone, and we think that isolation isn't good for a pack animal. But packs don't have to be of the same species. So another option might be a cat... except for the fact that I'm allergic to cats.
I searched for "hypoallergenic cat" on Google and the first entry is Allerca. I went to their website and was absolutely shocked. The cheapest one is $7950!!! And on top of that there is a 6 month waiting period. I don't suppose this is a breed that you'd find in shelters.