There's a lot of rare songs...
Let's begin with rare explicit album from the Philadelphia band The Bloody Stools called "Meet The Bloody Stools" released in 1991. It was recorded most likely in 1989. Richie played on guitar and sing backing vocals in most tracks, JBJ backing vocals are not confirmed officialy, but it was widely rumored.
Another album with a huge Bon Jovi contribution is Lance Larson "Songs for the Soldier":
More to come...