Nevada does this. If you are concealed carrying a gun not on your permit, then you are illegally carrying the gun. This came up in the Erik Scott case where he was carrying a Ruger that was not on his permit.
http://www.lvrj.com/news/officer-tes...103943584.html
In Nevada, you can have multiple guns on your permit, but you have to qualify with each. I don't know if there is a limit or not.