Can I re-write a book from my back list the same way Def Leppard re-recorded songs and now owns their rights?

Def Leppard, a band that provided much of the soundtrack of my youth, has re-recorded its backlist in an effort to regain financial control of their music.

With newly recorded "forgeries" of "Pour Some Sugar on Me" and "Rock of Ages" now available, the quintet has begun a series of re-recordings of its catalog material and "wrestled control of our career back" from the Universal Music Group, which frontman Joe Elliott says the band refuses to deal with "until we come up with some kind of arrangement" over compensation, especially for digital downloads.

I had no idea that this was possible, but apparently, it is. A record company pays musicians for the master recording of a song but not for the song itself. If a band wants to record a new version of the same song (or attempt to record an identical version of the same song), then the band retains complete financial control over their new version and can do with it as they please, including allowing it to compete for sales with the original version of the song.

I find this fascinating.

Curious about the results, I purchased the re-recording of “Pour Some Sugar On Me” in order to assess the performance. Though it’s a creditable rendition of the song, it’s clearly not the same song that blasted from the windows of every car in the summer of 1987.

I think I’ll be sticking with the original.

But this led me to wonder:

Would this strategy also work in publishing?

Could I re-write my first novel, Something Missing, either word-for-word or perhaps slightly differently, adding or subtracting from the story as I wished, and create an entirely new work in a legal sense? 

Unable to read my books after publication because of my preternatural sense of perpetual dissatisfaction and an incessant need to revise, a strategy like this might allow me to take a book that I wrote a decade ago and refresh it, making the necessary changes that are now obvious to me thanks to an improved skill set and more finely honed authorial instincts.

I’m not necessarily interested in doing this, but is it possible?

Could I publish the new and improved Something Missing that would compete against the original version of the novel?