Here's a good one that I had mistakenly assumed had already happened: William Basinski and Tim Hecker. They both have sounds that would go nicely together but I think they'd also be a good pair to push each other's boundaries.

Liz Harris and Phil Elverum.

Is this just hypothetical, because if so even though he's gone I wonder what Beefheart and Waits working together would have sounded like?

This is hypothetical, yes. I'm not sure if Waits would really bring anything to the table tbh, not to mention that Beefheart was kind of a dictator-esque bandleader so he might not even let him.

Their voices are so similar I think it'd be unnecessary. If we count their backing bands that would be something though.

It's true they could be very similar, but still, I think it would be interesting given all the weird soundscapes Waits works with and bringing even the old elements of his earlier jazz and blues into play. Beefheart sings "Small change"? Maybe Waits tries "Moonlight on Vermont"?

I also think Taylor Swift and Nicki Minaj, as I only have the one bullet...

The word unnecessary comes to mind again...

Flying Lotus and Thom Yorke. FlyLo could produce Thom's Hip Hop debut, and Thom could do some rapping, à la A Wolf at the Door.

Kind of a joke, and I know Thom featured on FlyLo's Cosmogramma, but a full album between the two could be really good.

What's unnecessary?

If they were to just sing each other's songs they don't really need to come together for it, I'd rather see them do something new. I think that both of them are above relying on cover songs to make an album (though Waits has did it with Orphans). I don't think that the style of music they play would be fitting for two voices, really. Although the more I think about it, the more interested I am in seeing where it would lead.

Franz Ferdinand and Sparks.

....oh wait.