So about half way through the show, Mick Jagger would announce "Okay, time to have our guest artist up here. (He gets handed an envelope and opens it) "Dave Johnson from Brooklyn New York, get up here we need a drummer!"
The crowd looks around and sees one of them making their way towards the stage,
roadies lift him up onto the stage and the drummer hands him the drumsticks. Keith plays the first chords to Jumping Jack Flash and Dave jumps right into his dream, of actually playing drums live with the Rolling Stones. I think the crowd would go nuts. I would.
The system for this would be a lottery entry where the contestants would just upload videos of them playing whatever instrument to whatever song. Management would pick the top 3 or 4 but the band members themselves would make the final decision as to the winner.
You would actually be able to say "The Rolling Stones chose me to play live with them for one of their songs. Just search Youtube: "Dave Johnson, Rolling Stones, Madison Square Garden."
Each city on the tour would get one song with a guest player sitting in. And again, just using the Stones as an example, any band could do this.