With An Awesome Wave, their Mercury Prize-winning 2012 debut album, Alt-J went from 0 to 100 real quick, transforming from anonymous schlubs into world-famous rock stars. They did so by forging a strikingly unique brand of prog-rock, approachable in its familiarity yet unapologetic in its weirdness. The band was formed at the University of Leeds and signed to Infectious Records after relocating to well-known academic hub Cambridge, and they’ve never disguised their own egghead tendencies. An Awesome Wave struck on some unholy amalgam of Radiohead’s ominous postmillennial electronic stadium rock, the Beta Band’s space-age digital folk, Sigur Ros’ sublime glacial soundscapes, James Blake’s post-dubstep pub balladry, Sufjan Stevens’ gently pastoral orchestral suites, and — thanks especially to singer Joe Newman’s pinched nasal bleat — the jangling jam-band grooves of Dave Matthews Band. The result was a Rush for the internet age: densely layered, virtuosic, and fantastically spacey yet also as introverted as an undergrad immersed in his handheld devices. It was a polarizing sound, but those who gravitated toward it swore by it.

Perhaps this shouldn’t be surprising at a time when the 12-sided-dice-worthy fantasy epic Game Of Thrones is the most voraciously consumed series on TV, but it still seems remarkable that Alt-J’s gloomy, intricately woven art-geek debut somehow scanned as pop. They appeared to have pulled off an impressive balancing act, corralling their oddest impulses into tightly wound dynamic structures and topping them off with around hooks that lingered in your consciousness whether you wanted them or not. In truth, they were just being themselves; An Awesome Wave caught on in a way that desperately pandering music never seems to muster. As a result, Alt-J seem primed to keep rising by simply doing what they’ve always done. And aside from the departure of founding member Gwil Sainsbury, that’s what they did, conceiving the follow-up to An Awesome Wave by experimenting together in a living room. Still, plenty of bands have stumbled into success by standing out then made the mistake of trying to maintain popularity by blending in. If such thoughts ever crossed Alt-J’s minds while crafting This Is All Yours, the sophomore LP they’ll release next week, it’s safe to say they went all the way in the opposite direction. This Is All Yours is a weirder, darker, more intensely singular piece of work — and better to boot.

If An Awesome Wave established one of rock’s most unmistakable signature sounds, This Is All Yours aims to push that sound beyond recognition. The first two songs Alt-J previewed from the new album hinted at its massive scope: First came “Hunger Of The Pine,” a creeping electro-orchestral dirge with a jarring surprise sample of Miley Cyrus singing, “I’m a female rebel!” That was followed by “Left Hand Free,” a carefree blues-rock goof that came about when Alt-J tried to write the least Alt-J song possible. Just about the only element the two songs had in common was Newman’s squawking gurgle, but that voice proved to be enough of a through-line to hold such disparate sounds together. As keyboardist Gus Unger-Hamilton noted in our recent interview, the band was well aware that Newman’s voice could function as glue for whatever experimental impulses captured their fancy. The rest of This Is All Yours makes full use of that freedom to explore the wide territory between those first two singles.

Among the results is “Every Other Freckle,” a gnarly electro-acoustic seduction that somehow also works as a rap beat. Hip-hop rears its head again in the hi-hats and scratches that mingle with what sounds like a music box in “The Gospel Of John Hurt” — at least until the track bottoms out into a halftime syncopated ceremonial sing-along. (That one’s about the birthing scene in Alien, by the way.) There is also “Warm Foothills,” a celebratory Sigur Rós slow-build gone full “Zip-A-Dee-Doo-Dah.” The Jonsi vibes return on “Bloodflood Pt. II,” which resembles a bigger, brassier version of Coldplay’s attempts to infuse electronic sounds into mournful arena rock. “Pusher,” meanwhile, is a barebones folk song; with just Newman’s voice and little more than an acoustic guitar, it retains all the oddity of Alt-J at their most expansive. And don’t forget the spooky “Intro,” a tune that approximates the Benedictine Monks Of Santo Domingo De Silos playing acoustic arpeggios in The Matrix, or the utterly unexpected cover of Bill Withers’ “Lovely Day” that emerges at the end as a secret track. It’s hard to call such a somber album a thrill ride — and in fact the album grows wearisome in the middle due to so many murky selections in a row — but what it lacks in uptempo tracks it almost entirely makes up for in surprise left turns. It sometimes feels like an album to be appreciated more than enjoyed, but there’s so much to appreciate about it.

If This Is All Yours has a unifying theme beyond Newman’s lizard-person voice, it’s a trio of tracks inspired by the Japanese city of Nara, where deer run free through an urban environment. “Arrival In Nara,” “Nara,” and “Leaving Nara” form a triptych of sorts. They serve as a fine showcase for what Alt-J can do sonically, seamlessly synthesizing styles and reminding us how dynamic a band can get while rarely rising above a gentle glide. We aren’t dealing with monsters of rock here, yet they manage a graceful sweep that feels like a drone camera hovering over all kinds of beautiful scenery. That trio of tracks provides This Is All Yours with its defining lyrical turn too. On “Nara,” Newman eventually settles into the refrain, “Love is the warmest color,” asserting that humans should be allowed to do whatever they want as long as they’re not hurting anybody else. It’s a common sentiment in this increasingly individualistic day and age, but few bands exercise their freedom like Alt-J. They’ve used their massive platform to deliver exactly the labyrinth they wanted to, and more people than ever seem ready to follow them into it. It’s worth wandering through, if only to marvel at such a willfully quirky band’s ability to charm the masses.

This Is All Yours is out 9/23 on Infectious/Atlantic. Stream it at iTunes.