I'm not a BJJ expert by any stretch of the imagination, but I do have a keyboard so here is my .02
I go to two different gyms now. One I go to roll at (and do a little standup) and the other I go to do primarily standup and ground and pound, and roll there sometimes. Thanks to Gray, I went to SIMGO in Las Vegas for a couple of days while I was there and Sim showed me some x guard and butterfly stuff that I haven't seen before other than on videos. I got my ass kicked by new people that rolled differently and did different things than I was used to. I tried some butterfly guard against them, having never done it before. I met some really great people. I went to VA to Master Eddie's seminar by myself not knowing anyone there, and having never done a 10th planet move in my life. I rolled with a guy from VA who was great and he showed me some stuff. I got to drill a technique with a 10p guy and learned something. I am trying to get to the East Coast training camp for at least one day this year. I would love to go to a moon sometime and learn as well. If money was no object I would travel the world and train in every discipline.
The people at both gyms seem to understand what I am trying to do, just learn and hopefully get better. No one has ever said a negative thing to me, more often than not they have questions about what it was like and want to see what techniques I was shown. They also like to see the collection of tshirts I am starting to get from different gyms. At the one gym we get several travelling guys, they bounce all over the place, they are great to train with. I can't wait to see what people will show me.
The only reason I would see an instructor telling you not to go to more than one is if they are looking out for you. I don't know your skill level, but if you are just beginning it might be best to stay at one.