Answer:
Well, if you really, and I mean really have to fit a lot of people in a room, consider that the average grown person can squeeze themselves into maybe 5 cubic feet of space. Then you pack these people into boxes that big and stack them in the room. If your room is 50 feet by 50 feet by 10 feet tall, you have 25,000 cubic feet of space. Divided by five, it's 5,000. So you have 5,000 angry, suffocating people packed this single room. That would be a BIG party, but not a very fun one.
In all seriousness, you have to ask a fire marshal about the maximum legal amount because there are a lot of factors.