Not just multi-party, but packed. I'd been pre-pandemic, and usually there would be a few families. This past trip, we did a couple of ceremonies that must have hit peak times, because there must have been 30 of us in there.
Typically one person is chosen, usually a child, but not always. I think we did 3 or 4 ceremonies, and at one of them an adult woman was chosen.
Occasionally, they will do a double ceremony - my son and niece got to do it together this trip, which was very cool for them. I don't know what made them get picked other than we went at a time when it seemed pretty dead, and the kids were very animated in their excitement around HP, and enjoyed observing the details of the waiting room. At the start of the ceremony, when the wandmaster asked, "what is your name?" my son answered, but it turned out the wandmaster was talking to my niece who was standing right in front of my son. Then he asked their relationship, and called them both forward. I don't think it was intended to be a double ceremony, but he kind of went with it.
I think you'll have a better chance of standing out if you go at a time when there's not a big crowd, and get there early. I can't say for certain, but I think the TMs in the waiting area might be observing the guests and passing on recommendations for the ceremony. If my hypothesis is correct, people who show up earlier have a better chance than those who slip in at the last minute and don't get to make any sort of impression on the wait room TM.