In the chat before yesterday's session, Paul Clarke posted this:
" I'm planting this little 'bomb' to see if it creates any buzz among you: Mudcat Zoom session, with a theme of songs/tunes within songs. Songs that reference other music would be sung, and broken off at the appropriate point for [I'd moot] another performer to render the mentioned tune, or in the case of a song, to segue one after the other. I think I've listed, or been triggered to note but forgotten to[!], about 15 of these, but with all the Cat brains jointly at work on the idea, I'm sure many more would crop up. Perhaps needs a couple of weeks' notice, esp. to tout for the musical partner, but worth considering?
When I get back, I may ask the question again, with some examples. Meantime, what does Joe O and others think of it."

That could indeed be fun, but it will certainly need considerable advance planning to identify the relevant songs and tunes and the personnel to perform them.

Paul, if you see this, please post your list to save us racking our brains for examples that you've already thought of.

The only one that I can think of immediately is Byker Hill and Walker Shore referring to "the tune of Elsie Marley".