In Gamma Phi Beta, AIs are initiated with the collegiate chapter which sponsors them, which is most often the chapter which is the closest geographically. In my case, I "wasn't allowed" to initiate with the Long Beach State chapter, or my Big Sister's chapter at University of Southern California. I was initiated into the University of San Diego chapter because it's just down the road from my house.
I also prefer having a collegiate chapter designation. I'm not sure I would be keen on an AI designation or dual-designation. Though, when looking at a list of Alpha Phis, it's always cool because I can easily spot all of the AIs!
.....Kelly