I once played a house party where we did this.
It was just two piece - bass and guitar.
We practiced as many songs as we could 2 or 3 times through, and printed the lyrics. All the lyrics went into a folder.
We set up PA at the party and told people to pick anything out of the folder.
It was awesome. Everybody loved it. There were no expectations that the cover songs were faithful to the original, and nobody cared when mistakes were made. We were kept busy by the guest singers for hours - longest set I have ever played. Took a break and people want to keep singing, so we did it some more.
It's definitely not rock star glory, but it was a lot of fun and really easy to do.