I've been digging the two Tim Ries 'Rolling Stones Project' discs for a while now, and you might not be aware of them.
Tim Ries is in the Stone's touring horn section (great player), and he set out to 're-imagine' quite a few classic Stones tunes. The first disc is more of a jazz take on things (Satisfaction with Scofield and Patitucci, and I think Brian Blade on drums.. not sure there) is KILLER, and to give you an idea, they do Street Fightin' Man as an up-tempo jazz samba!
The Stones dug it so much that they got involved, so Charlie, Keith, Ron, and even Mick make appearances.
Just like the amazing Herbie Hancock 'Imagine Project', this really does come across as a labor of love, and there is a lot of joy in the recordings.
The second disc takes a 'world music' theme, Here is a Youtube of a sort of 'flamenco' version of Jumpin' Jack Flash'.
I prefer the first disc, but the second is cool also... DeJohnette is on a few tracks... amazing.
Anyway, FYI... interesting stuff
Tim Ries & Rolling Stones Project 2 - Sara Baras - Jumping Jack Flash - YouTube
Jay Anderson on DB on this track. The actual performance starts at the 3 minute mark.
PS Can you imagine what Tim said when Keith Richards and Charlie asked if they could be a part of this. Hah!.... kind of like uhmmm.....YES.