I’m sure I’m missing more examples, but space got a little cramped.
Edit: added Saru for Admiral Patrick, and in doing so, had to add SNW Kirk to hide Saru’s cropped head… also now featuring a conveniently placed Zora… plus Kira and Jadzia’s beautiful rendition of “Allamaraine” followed by drunk Bashir for Lopen’s Left Arm… more backup vocals from “Unnamed Klingon Chef” from DS9 in lieu of Gowron from the Klingon language program for PrinceWith999Enemies… including the DS9 do-re-mi quartet for CelloMike… rounded out with blooper reel Gene and Danilo for aeronmelon.
Since it doesn’t have to be 100% in-universe. There’s also that one blooper from TNG’s Up the Long Ladder where Worf, Danilo Odell (Barrie Ingham), and Gene Roddenberry are singing a jaunty folk song:
@ 1:50
https://m.youtube.com/watch?v=4NOM-kLfDR8
Great blooper reel! Crammed them in for ya.
Damn, you need a bigger viewscreen.