I can think of several groups that were MOSTLY The same as previous groups (Arcadia was almost Duran Duran, Bell Biv Devoe was almost the New Edition), but if it has to be all but one member…
After the 1971 Islands tour, everyone in King Crimson quit, except guitarist Robert Fripp, who had alienated everyone (a recurring theme with KC). Singer/bassist Boz Burrell, sax player Mel Collins and drummer Ian Wallace all joined British blues guitarist Alexis Korner in a new band called Snape.
They started calling themselves “The Jacksons” unofficially in the mid-Seventies when their youngest brother Randy started singing with them. They didn’t make it official until they left the Motown label (apparently Berry Gordy owned rights to the name “Jackson 5.”)…
I’ve seen The Band more than a few times. Rick Danko, Levon Helms, Garth Hudson, Richard Manuel (only once) - they did quite well sans Robbie Robertson. I’ve seen The Last Waltz - it’s great stuff. I’ve seen Robbie Robertson solo; he wasn’t good.
They lost Peter Gabriel (who is fuckin’ awesome live and studio), Steve Hackett (awesomly terrific guitarist) and they were, at least till 1985 or so, one of the greatest Prog Rock Bands.
By the end of the Sex Pistols brief moment of fame they only had Cook and Jones still in them. Sid was dead and Johnny Rotten had left.
Cook and Jones then picked up session musician Andy Allen (who had also been a session musician for the collapsing Sex Pistols) and formed The Professionals.
So actually, depending where you draw the line, The Professionals are either different or identical to the Sex Pistols.
1960’s band Manfred Mann reformed in the 1990s as The Manfreds without founder member Manfred Mann. Manfred himself formed the Earth Band in the 1970s later retitled Manfred Mann’s Earth Band.
Tears for Fears (who wrote and had a hit with the original version of Mad World) were basically a duo of Roland Orzabal and Curt Smith. Smith split for most of the 1990s while Tears for Fears continued with just Orzabal. And then - everyone likes a happy ending - Smith rejoined in 2000.