Kim Thayil doesn't anticipate ever using the Soundgarden name for any new music or tours.
Thayil tells the Seattle Times that he wants to make music in the future with Matt Cameron and Ben Shepherd, but without Chris Cornell they would not use the band's name. He says, "I don't know really what kind of thing is possible or what we would consider in the future. It's likely nothing. The four of us were that. There were four of us and now there's three of us, so it's just not likely that there's much to be pursued other than the catalog work at this point."
Thayil, who's been the band's archivist over the years, adds that he's working with Sub Pop on possible compilations and live albums, plus the release of other unreleased material. He's also talking with Universal Music, which owns the rights to their A&M catalog, on some more projects.