I have two females and a male, and honestly my two females have gotten into "fights" at least three different times (once when I couldn't call off the older female and actually had to physically seperate the two). Chloe hasn't gotten into a fight with Blackie yet, although I have to make sure food is non existent when they are around each other.
A couple of years ago when my trio consisted of Blackie, Rose, and a neighbors female Malamute, it was again the two females that would get into squabbles. Blackie and the Mal got along wonderfully and never fought (except over food).
All in all, I think it really boils down to dominant and submissiveness. Blackie and Loupie were both dominant dogs, but since they were of opposite sex they got along okay. In Rose and Chloe's relationship Rose thinks she is dominant, but Chloe also thinks she is and there is a lot of posturing and things that would be fights if Rose didn't have such a good recall.
Good luck picking out a new addition!
It really is loads of fun.
Oh, and Chloe is full of bad behaviors. LOL Blackie and Rose haven't picked up on any of them because they've been well trained. I just wish Chloe would pick up on their GOOD behaviors, but alas, it is not so.