The Miracles had a #1 single (“Love Machine”) without Smokey Robinson- does that count?
I don’t know how successful they are now, but Journey found their new singer on youtube. I’m not much of a fan, but it’s a pretty neat story and he sounds very close to what was a distinctive voice.
That brings up a question- how do you decide which bands have been “successful” with their new singer?
Is it record sales? Then many of the bands mentioned earlier (Deep Purple, Genesis, Chicago, Van Halen, Jefferson Starship) qualify. They’ve had big hit singles and/or gold albums with more than one singer.
But Journey has only had real commercial success with Steve Perry on lead vocals. They were a minor prog-rock/jazz-rock band when Greg Rolie was the singer, and they haven’t had any hits since Perry left (though you’re right- the new singer sounds very good, and Journey remains a popular live act).
Similarly, all of Boston’s successful recordings have Brad Delp on vocals (no disrespect to the newer guy). And Styx has never had a hit without Dennis DeYoung (though they still draw good crowds on the concert circuit with Dennis’ replacement).
(Ritchie Blackmore’s) Rainbow was pretty successful with Ronnie James Dio on vocals, then MORE commercially successful with Joe Lynn Turner on vocals.
They did alright with Graham Bonnet singing as well.
Has anyone mentioned Nightwish yet? I believe their most recent album, with the new singer, is their most commercially successful.
Alice in Chains are doing fairly well without Layne Staley now. They took years off, but finall replaced him with William Duvall.
Huh. I was going to post that they did continue to use the name Small Faces anyway for their first album with Stewart. Fortunately, I checked before posting, and discovered that this was a concession to the record company that was done only for the U.S. release, and in the U.K., First Step was credited to Faces. Never knew that.
K-Paz de la Sierra’s lead singer was murdered by the drug cartel, his brother replaced him and they are doing great!
But McDonald never sang lead for Steely Dan. Or were you intending to describe the success of the Doobie Brothers after changing lead singers? Because I think that would count.
For another suggestion:
Possibly Bad Company could count, although they were never quite as successful as in their first incarnation. Also, the changes were almost to a completely different band that only shared the name. (And to further mix it up, the original lead came back years later).
Damn you guys got the first ones I was going to psych you out with (the obvious ones): Deep Purple, Black Flag, Genesis.
How about Bob Wills and (his) Texas Playboys? For you old-timers, Count Basie Orchestra had a few 
The Beatles did OK after Paul’s replacement after he died.
Sorry.
Iron Maiden
Annihilator changes singers regularly - the heart and soul of the band is lead guitar Jeff Waters. Who also happens to have an ego the size of my… well, it’s big anyway. He regularly rotates drummers, singers and bassists out when they threaten to have gasp fans and recognition of their own.