His Wikipedia entry indicates that he wasn’t confident in his singing voice at first, but then sang lead for the first time on the 1977 KISS song “Shock Me,” which he wrote (and may well have sung on other songs before leaving the band).
Glenn Frey and Don Henley were the primary lead vocalists for the Eagles, but Randy Meisner, Bernie Leadon, Don Felder, Joe Walsh, and Timothy B. Schmit all also sang lead at least once on the band’s original run of albums.
Edit: mostly ninja’d by @EinsteinsHund because I was slow in composing this.
Another that comes to mind: The Moody Blues. Looking at their best-known lineup from the late '60s and '70s, Justin Hayward, John Lodge, Ray Thomas, and Mike Pinder all had turns as lead vocalist, and Graeme Edge contributed spoken-word vocals on a number of songs.
I have to admit that at first, I misread the OP and thought that bands with at least three lead singers count, not only bands where everybody sang. So some of my examples don’t count, sorry.
Wings
In an attempt to pretend Wings was a real band and not just Paul’s backing band, all 5 members took at least one lead vocal on the Wings at the Speed of Sound album.
Paul: 6
Linda: 1 + co-lead on 2 others
Denny Laine: 2
Jimmy McCulloch: 1
Joe English: 1