John drops out, is replaced by George^2.
Ringo drops out, replaced by Pete.
Paul drops out, replaced by Brian.
George drops out, replaced by Billy.
George^2, Pete, Brian, Billy.
You could argue they are still the same band as 3/4 of them each played with original members. Billy is the first to have never played with any of them.
Now... if George^2, Pete, and Brian get replaced, no, it's not the same band.
I would add that also there should also be a connection between the art/music for them to be considered the same band
For example: Black Sabbath only changed their vocalist and they sound like two, quite, different bands. On the other hand, Iron Maiden also changed their vocalist and they sound like the same band with both Dickinson and Di'anno.
But you have a pot of soup and at the end of the day you have a little left and so you add more ingredients and fill the pot back up. You do this for years. Is it still the same pot of soup?
I saw them for free last year and it was pretty whack with so much flag waiving super the troops patriotism shit and none of the members. Time to wrap it up
Reminds me of that time in the early-70s when David Bowie was swooning backstage while meeting The Velvet Underground, only to be informed a little later that he'd been talking to Doug Yule, who replaced John Cale then took over as frontman when Lou Reed quit the band, and if I'm not mistaken with the timeline, even guitarist Sterling Morrison and drummer Moe Tucker had already also split.