“What’s this band sound like?” asked a passer-by at T.T. the Bear’s Place on seeing the Continental Drifters’ name on the chalkboard. “Rock band from New Orleans,” replied the guy standing outside the club. “Lots of songs, lots of voices. If you like music, you’ll like them.”

Sure, it’s odd that a member of the Drifters — in this case, singer/keyboardist Peter Holsapple, who was resting outside T.T.’s before the show — still has to explain what his band sound like. But his description is as good as you’ll get, since the Continental Drifters — after 10 years, three albums, a dozen-odd personnel changes, and a move from Los Angeles to Louisiana — have outgrown the “roots-rock” tag. They write resonant songs, sing beautifully, and change styles with every other song; and they’re so damn informal about it. This is a band who want to bring the world into their living room.

They wound up playing two area shows last weekend, Saturday at T.T.’s and Sunday at the newly opened Narrows Center for the Arts in Fall River (a converted mill located about four blocks from the site of Lizzie Borden’s famous ax work). A homecoming of sorts for singer Susan Cowsill (who grew up with her singing family in nearby Newport), the Fall River show had more of the living-room vibe. It started acoustically, with Holsapple playing accordion and Cowsill dancing with some toddler cousins up front. During a cover of Richard Thompson’s “You’re Gonna Need Somebody” the band took a short pause, picked up electric instruments, and shifted into loud-rock mode, with Robert Maché getting in some serious ax work of his own.

At T.T.’s they were battling the elements, with Holsapple getting hit by food poisoning (thus singing less than usual) and feedback problems derailing a couple of songs. But the two shows had many of the same peaks, including Holsapple’s punk-with-washboard “Don’t Do What I Did” and guitarist (and Bangle) Vicki Peterson’s defiant rocker “Na Na.” The a cappella break on Peterson’s “Watermark” and Cowsill’s ballad “Snow” were both lump-in-throat material. And in a nice bit of synchrony, bassist Mark Walton sang “Tomorrow’s Gonna Be” — a spooky, Southwestern-style tune about late-night bar crawls — just as T.T.’s was announcing last call.

Bill Janovitz has been a busy guy lately. Along with playing the occasional Buffalo Tom gig, he’s wrapped up an acoustic solo album that’s being released on Spin Art next month. And he’s got another album’s worth of as-yet-unrecorded songs for his new band, Crown Victoria. During Saturday’s opening set at T.T.’s, those songs ranged from sounding a little like Buffalo Tom to sounding (on the churning “Fireworks on TV”) exactly like Buffalo Tom. The difference is more in arrangement, with Crown Victoria abjuring BT’s full-throttle approach in favor of fully integrated keyboards, harmonies, and Janovitz’s Sticky Fingers–era Stones roots.