From season 2 of The Muppet Show:
Impressionist Rich Little performs a 3-song medley of songs from musicals:
1. Rich, as Gene Kelly, sings the title song from "Singing in The Rain". Fozzie Bear (Frank Oz) chips in, and Rich pauses to do Winston Churchill (since the show tapes in London) and John Wayne.
2. Rich, with Kermit (Jim Henson), performs "Well, Did You Evah?", as Frank Sinatra & Bing Crosby (from "High Society").
3. As Maurice Chevalier, Rich serenades Miss Piggy (Oz), standing in for Hermoine Gingold, with "I Remember it Well", from "Gigi".
I'd post the complete episode, but the only copy available on Dailymotion resorts to the trendy tactic of pushing the camera back & forth for unnecessary close-ups in order to evade the copyright police.