As it turned out, every one I picked for an instrument can actually sing and be the frontman/woman as well, so they could end up being very Beatlesy.
Drums: Has to be Dave Grohl. Coolest man alive(tm) and nicest guy in rock, apparently. Plus, he was in Nirvana AND fronts the Foos, along with sometimes being in QOTSA and Them Crooked Vultures. He is, in fact, my main reason for hoping this could happen - the guy loves to collaborate.
Bass: Speaking of guys who love to collaborate - Jack White. I love the Raconteurs' second album and I can't think of a better bass-led tune than Seven Nation Army by the White Stripes.
Lead Guitar: I nearly picked the person I'm putting on rhythm guitar for this, but decided I couldn't really look past Matt Bellamy of Muse. Epic, epic stuff, plus he can sometimes sit in on piano if my pianist fancies standing up to sing.
Piano: Tori Amos. No competition. Nobody makes a piano sing the way she does. Haunting, joyful, sad, explosive - I'm not entirely sure she's human - in a good way.
Rhythm Guitar: A slightly left-field choice, but I think his acoustic style could blend interestingly into the rest of the band and I love his sound - Sam Duckworth of Get Cape. Wear Cape. Fly fame.
Vocals: Anybody who knows me knows it's Eddie Vedder. Of course it's Eddie Vedder. But I've also opted to add Tanya Donelly of Belly and Throwing Muses as I reckon the two of them could produce something amazing together.
There you go - my own personal supergroup. If any millionaires want to throw me a surprise 40th birthday next year, this would be a REALLY good present.
What's your dream supergroup?