As some have mentioned already YES you can have multiple permits. The key is the state you live in is the resident permit and the others would be non-resident, mind you not all states issue non-resident permits. I got a VA permit when I was stationed in Norfolk. It was a resident at the time. When I moved to OK I called them and had it change to a non-resident. I will be getting a resident OK here soon.
The only reason someone would really need multiple permits is to be covered in states that one permit may not be valid in. If you travel around the country then its a good idea to have them.
A good book to get, I've been getting them for 5 years now, is the "Travelers Guide to the Firearms Laws of the 50 States". I believe the OCDO homepage has a link to it if not a google search will get it for you. I never travel without it as I usually travel to 5-10 states a year.