One of my favorite bands, Level 42, had this issue.
The classic lineup - Mark King on bass and vocals, Mike Lindup on keys and vocals, Phil Gould on drums, and Rowland “Boon” Gould on guitar.
An early incarnation of the band featured Dominic Miller on guitar, who later found fame as a session player and Sting’s axeman.
Level 42 rode the jazz-funk wave in the early to mid 80s in the UK and Europe, and even had a Top 10 hit stateside with “Something About You.” After the follow up album, Running in the Family, was released, the band earned an opening slot with Madonna on her American tour. Both of the Goulds left the band citing exhaustion.
Mid-tour they replaced Boon Gould with Steve Topping, I think. Phil Gould was replaced with Neil Conti (formerly of Prefab Sprout).
Their next album, Staring at the Sun, was recorded with Dominic Miller on guitar (who was supplanted by permanent replacement Alan Murphy, who played with Kate Bush and Go West) and Gary Husband on drums.
Sadly Alan Murphy died of AIDS in 1989, and the band disappeared for two years. They reappeared in 1991 with an album Guaranteed, with new guitarist Allan Holdsworth (yes, that Holdsworth, who was actually Alan Murphy’s hero). Holdsworth didn’t tour with the band more than a few dates - his replacement was Jakko Jakszyk, who appears on the album cover, uncredited, despite not playing a lick on the album.
The last “classic” album was 1995’s Forever Now that had Phil Gould returning on drums and the little guitar work by Danny Bloom.
They just released a new album. The only original member on it are King and Lindup, but Husband is back, who in truth has played with the band longer than Phil Gould, and the guitar seat is held by Mark King’s brother Nathan. (whew!)
INXS replaced Michael Hutchence with JD Fortune and didn’t do too badly - their commercial fortunes were faltering and the album did decently in Europe.
Joy Division lost their lead singer and rhythm guitarist when Ian Curtis committed suicide, and the three remaining bandmembers all took turns as lead vocalist. (Peter Hook is the lead vocalist on “Dreams Never End.”) Bernard Sumner emerged as the eventual singer, but had difficulty playing lead guitar and keyboards as he did in Joy Division. Drummer Stephen Morris recruited his girlfriend Gillian Gilbert to play Sumner’s parts (she knew most of the JD songs from following the band), and she became part of the band, rechristened New Order.