I can't speak for out there, but here in NH and ME, the law limits semiauto hunting rifles to 5 shot clips. .22 rimfire and pistols are excluded from that requirement.
My experience has been that usually the first shot is the one that really counts. Certainly there are exceptions to that statement, but a majority of the time, rarely do follow-up shots have much value unless the animal goes down and needs a finishing shot. Once a deer gets into high gear, most follow-up shots are a waste of lead. I don't think I have ever fired more than three times at a deer.