bands other than Sonic Youth with three or more recurrent vocalists
 

enlighten me

the beach boys

the velvet underground
the beatles

The White Stripes.

Nirvana

no wait...

jack, meg, and...?

Old Skull

Teenage Fanclub is the only one I can think of off the top of my head.

Wu-Tang Clan.

thinking fellers union local # 282 (4)
boredoms (at least 4)
charalambides (one era had 3-4, usually just christina though)
acid mothers temple (depends on the era, but there's been many vocalists on tracks before..)
sun city girls (3)
fire on fire (5)
cerberus shoal (6)
polysics (kaja kaja goo ep era had 3)
koennjihyakkei (I dunno, probably like 5; they're usually harmonizing though)

and you, and you, and you, and you


on a more serious note, excepter has curently three vocalists

the beatles
the monks
os mutantes

thats me thinking of at least 3 LEAD vocalists, cause otherwise there'd be a shit load more, vivian girls, sleater-kinney, etc...

pink floyd
smashing pumpkins
bikini kill
the breeders
the pixies

sleater-kinney had 3 lead vocalists, but only for the first album

the pastels

spice girls

Mission of Burma.
Fugazi.


...Hanson?

reggae vocal trios

Abyssinians
The Original Wailers feat bob marley peter tosh and bunny wailer
Israel Vibrations
Black Uhuru

and they do it like sonic youth, alternating each artists individual songs, though since it is reggae, the other brothers sing harmony

I wasn't really thinking of bands that have changed vocalists 3 times, by the way.

Doesn't count, for the reason above, plus Wright didn't sing often enough to be classed as 'recurrent', in my opinion. Same can be said of George Harrison too maybe.