Meet market

The key to making new friends is making friends with people who have friends they are willing to introduce you to. I envision a party where the host invites 3 or 4 people with the caveat that they have to bring someone the host or the host-invitees don't know. So theoretically, the party would be a good mix of people who know each other and don't, so you'd avoid the problem of having a couple of people at a party who don't know anyone except the host, but also not so many new people that the host herself is flustered with trying to make conversation or connections between all of the guests.