I'm gonna dump an idea I had awhile ago onto the web. I've seen similar things, but nothing that takes the form I'm going to describe.
Still, I wouldn't be surprised if something like this has been done before.
I've dubbed it the Open Source Band. It's built around the Creative Commons License, specifically the Attribution-ShareAlike.
Boiled down to its essentials:
1. A Band Name is Chosen. This name is free to be used by any band/musician for performances or recordings. The name is completely hackable. Change it completely. Under no circumstances can it be trademarked.
2. A Website is Built. Registration is free, but contributors must get a special pass from a moderator. Regular registrants can post and add to the sheet music database. Contributors can upload sound clips.
3. Standards are Decided. Sheet music and sound clips will use common filetypes, carefully limited to ensure maximum compatibility among all involved.
4. Music is Created. Musicians write songs. They upload the songs to the website. In addition, they upload the components of a song (the separate parts before a mixdown). Participation is contingent upon accepting the terms of the license.
5. Music is Remixed. All different song parts are tweaked and chopped and remixed and reversed. New songs are formed. Those songs become a part of the Band's setlist, usable by all for any purpose: benefits, albums, concerts, soundtracks.
6. New Bands Form. Given enough interest among contributors, a Band Name might rotate, or a new one might be created.
What I really imagine is a concert poster. The lineup starts out SCREAMER in big bold letters and underneath that "Opening for" and underneath that SCREAMER and then "Followed by" SCREAMER'S SISTER and then REMAERCS and then "Next Week:" and then SCREAMER.
And every band plays something wildly different but wildly similar - some of the lyrics sound just right but a bit off, so people have trouble singing along. Riffs repeat, bandmates merge in and out, wondering if they're with the right version of SCREAMER and ultimately not caring.
And when the people leave the club and are walking to the Metro, they struggle to put it all together. Someone on the street asks if they liked the band and they wonder, "Which part of it?"
Not necessarily earth-changing, but at least a small bit of reverse branding. Instead of attempting to force a symbol to take on certain meaning, a symbol is morphed and twisted until it evokes a wide range of feelings and reactions and defies predictability.