Event and reception centers have room occupancy limits for a reason. Too many people make it harder to evacuate the room in an emergency. The problem is bad enough when you're dealing with random people trying to get into a hot party or convention. But what do you do when the event is really your wedding reception or a graduation party in a smaller room at a center that hosts multiple events? If you can afford security to allow in only those with invitations, that's great. (You'll see online advice about how rude that is, with no mention of how rude the uninvited guests are being -- hire security if you can afford it.) But, if you can't hire security, you still have options.
Design your invitations and RSVP cards to have room for only the names of the invited people. Don't put general identifiers like "the Smith family" if the Smiths tend to invite five people along with them when you were thinking maybe two would show up. Have the people's names pre-printed on the RSVP cards with checkboxes for whether they will or will not show up.
Many people get the hint, although some still do not. If possible, design the cards so that people can't write in other names.
Looking at Flexibility and Final RSVP Numbers
Another thing to do is wait until all the RSVPs are in. Invariably, some invited people will RSVP no, leaving extra room. If all you're dealing with are a couple of people who bring plus-ones or an adult child, you may actually end up having room for them.
This is helpful when those extra guests are people you know well or who have some other reason for sticking close to the invited guests, such as when your friend and his wife have just invited one of their older family members to live with them, or maybe they now have an exchange student staying with them. Maybe they don't want to leave that person alone, and if you have room, that could help them out.
Of course, a lot of the time those extra guests are just there because the invited guests didn't respect boundaries. When you're in that situation, it's time to be straightforward and tell the invited guests that you can't have extra people there. Occupancy limits, as well as catering and seating limits, require that you have only the people invited and no more.
This is a tough move because you have to be ready to disinvite people who insist your boundaries mean nothing. But, if they're treating you that way, that relationship already has some issues you need to address.
Invitation-only events can be difficult to pull together, and you need your guests to not add to the difficulty. It's easier said than done to be firm about limits, but you need to keep your event within the center's occupancy rules. For more information, contact the reception center for your event.