I have tried a few times by inviting people from different groups of friends to events with other groups of friends, but I can't think of a single time that it has worked out. Perhaps the closest thing to success that I've had was my Break-the-Octoberfast/Sober Octoberfest where I invited a few people who were new members of the ward and now they seem to be friends with some of the other people that I invited, but I don't know that I can blame any of that on my pretzels and cider.
However, I realized today that Facebook actually does pretty much exactly what I'm trying to do. I can make muse with my status updates, and all the witty people I know from all aspects of my life comment on my status and other people's comments. It's like a very brief gathering of all my friends. It makes me really happy. Maybe someday I can host a movie night for a few regular commenters. Or maybe I'll just continue to let them hide behind a sort of translucent anonymity, and I can just pretend we are all friends.