Well, hopefully somebody has already pointed out that there is no band that sounds like Primus.
I know that for many many years, if I played a CD on my computer it would always tell me the name of the band, the album, and the genre.... except Primus... Primus was THE ONLY band that would come up: Genre = Primus
I always thought that pretty much said it all. (I think it was Windows media player - somebody help me, somebody knows...)
ANYWAY - My opinion... Primus fans who are in need of new music usually enjoy Frank Zappa. If you haven't yet checked out Zappa, I'd recommend that. Not because anything directly reminds me of Primus - just a similar blend of music and wackiness maybe...