Anvil?
Comeback kids. Saw them in Sydney on Sunday night. Thoroughly professional bunch who have been together for 17 years with the same lineup. Played a few songs off this year’s How Big Can You Get.
He’s apparently big in Europe.
Cyndi Lauper - She’s So Unusual - Sold 5 million copies, contained 4 Top 10 hits and a 5th Top 30 hit. All over MTV. Followed the album up with a hit song for the Goonies soundtrack. The lead single from the follow-up album, “True Colors”, was a big hit, but then… poof gone.
Vanilla Ice - To The Extreme - Sold 7 million copies and had 2 (yes, there was a second hit) Top 5 singles. Followed up by flop after flop.
Asia - Their self-titled debut was supposed the most bootlegged (home-taped) album of 1982. Every damn song on that album got tons of airplay on hard rock stations of the AOR format. But “Don’t Cry” is their only song I can name that wasn’t on that first album.
Arrested Development had a big hit with Mr Wendel and another and then kept recording without another huge hit.
I’ve thought of one that meets my own criteria - namely, three or more songs from the same album that generated quite a bit of airplay but I’ve never personally heard other stuff by them on the radio.
Jimmy Eat World. Bleed American/Jimmy Eat World had the title track, The Middle, The Sweetness, and A Praise Chorus that I’ve heard on the radio more than a dozen times each. Haven’t heard anything on the radio from them since.
Missing Persons, the album was Spring Session M
Should’ve thought of them myself. They’re still around, though they went through a number of different line-ups. They’re finally back to the original 4 guys, and released a new album a year or so ago…but, you’re exactly right, their second album wasn’t nearly as big as their first, and everything else just sort of vanished without a trace.
Haircut 100.,. “Pelican West” i believe the lead Singer Nick Heyward went a little batty…
Love plus one… Fanstastic Day… a great great album…
EMF - Schubert Dip
Supertramp - Coming to America
You obviously never saw their “Indelibly Stamped” album. 
You obviously don’t mean this Supertramp!
You obviously don’t mean this Supertramp!
Not going to argue on the mediocre ('cause you’re kinda right), but I remember at least one song from their second album that featured on a TV show or two. But. . .yeah, I guess they are mostly known for that first album. It’s gotta be the chanting.
I’ll nominate Third Eye Blind. They had albums and songs after, but that first album had a ton of hits, and is arguably what they’re best remembered for (“Semi-Charmed Life” “Jumper” “Graduate” “How’s it Gonna Be”. Goddamn that was good).
Don McLean’s American Pie. Besides the truly huge title track, it had at least one other semi-hit (Vincent) and several other very good tracks. I’ve found most of McLean’s other albums unlistenable – he sounds too much like a lounge singer on his other albums.
I sure screwed the pooch on this one!
Humbly retracted…
Be honest, how many people even know that The Power Station had a second album?
I didn’t. Personally I’d rather have a second Arcadia album (the only reason early Duran Duran songs sound better than So Red the Rose is the youthful energy.)
I don’t think I would count EMF, and not only because nothing came close to “Unbelievable” (or as I like to think of it, “Crumbelievable.”)
IIRC, they didn’t even have Schubert Dip finished when “Unbelievable” exploded. Sadly, their career had already peaked BEFORE their first album was even released.