In my experience, families don't entertain more then one possible match a time. After the first interview, they'll take some time to decide whether they want to pursue the match they most recently met, and if the answer is no, then they'll look for another match. They don't generally have multiple first meetings before deciding on the follow up meetings.
Once they decide that they'd like to meet a girl and her family for a second time, meetings will take place usually in both the grooms and brides homes. Generally additional extended family members will be invited to help size up the situation. Sometimes the bride or groom will be part of the meeting as well.
These meetings are a bit more laid back, unscripted, and less formal. Although you're still expected to wear a fancy dress, because impressions are still being made and it's important that the entire family presents well (remember What Not To Wear).
Generally after this second and third visit (one to each household) a decision will be made. It's quite likely that the bride and groom still haven't been alone together to talk. We tried this with the family I was with, and after a few minutes, the sister of the bride went into the room with the bride and groom, and, worried that the groom was out numbered, I asked for permission to join them. Naturally the bride's sister was the one doing all the talking and the bride and groom were just sitting there silent. So it ended up with just the brides sister and I talking.
I tried sharing some information about the groom, like about what kinds of things he was good at, what dishes he prepared well, thinking talking him up was a benefit at that point. After I got a sharp look from him, I realized it was better to keep my mouth shut. Then it got awkward, so I left them to their own devices. What do I know?
After we left, I asked the groom if he was upset with me for saying so much. He said not everything needed to be revealed before the wedding and that there should be some surprises for afterwards. I'm thinking that you'd want to put your strengths out there to help in the decision making, especially if you're interested in the other person. Don't you want to sell yourself a little? Again, what do I know?