Here's another Rolling Stones in the 80s video for you. On November 22, 1981 Muddy Waters was playing a set at the Checkerboard Lounge in Chicago. The Stones were in town because they were about to play the next three nights at the Rosemont Horizon.
There happened to be a camera taping the Muddy Waters performance and The Stones just roll into the club and take over the front table. Next thing you know Muddy starts calling them up on stage one-by-one until Mick, Keith, and Ron Wood are all jamming with Muddy Waters. I could watch this over and over.