Belle & Sebastian frontman Stuart Murdoch took the stage at Pitchfork Music Festival last month wearing white pants, a tight black T-shirt, and a black jacket, looking like a character from Grease or West Side Story in search of a dance-off. He did the running man, shadowboxed, jumped, and clapped. On the rare occasions when he strummed an acoustic guitar, he triumphantly lifted it skyward like Win Butler or Garth Brooks. He asked the men in the crowd to crouch down so he could see the ladies. He climbed into the audience during “Lord Antony” and clasped a man’s hand during the ballad’s passionate climax. (“That’s the first time ever I’ve let a man touch me,” he said, tongue presumably in cheek.) He pulled a girl on stage and danced with her before she read the spoken-word part from “Dirty Dream Number Two.” Later, he invited a whole slew of folks up there to wild out like they were at a Dismemberment Plan or Girl Talk show, eventually huddling them all together to coordinate hand motions and finger snaps.

Anyone who discovered Belle & Sebastian during the band’s introverted early years might have wondered: Who is this band? And what did they do with the shambolic bookworms who made If You’re Feeling Sinister? There were some connective threads — the hundreds-strong Peanuts dance party in the rain during “The Boy With The Arab Strap” was the apotheosis of early Belle & Sebastian’s chaste twee ideal — but the theatrical ensemble providing the soundtrack had become a different creature. Murdoch’s quip when he pulled the girl on stage was indicative: “Don’t be nervous or anything. Enjoy yourself. You should all enjoy yourselves.” A far cry from buttoned-down daydreams in cloistered churchyards, no?

The freewheeling-extrovert version of Belle & Sebastian isn’t exactly new. As the imminent compilation The Third Eye Centre exhibits, Murdoch and company left behind the library to get their Godspell on a solid decade ago. The double-disc set collects EP tracks and B-sides from Belle & Sebastian’s Rough Trade career, a sort of companion piece to 2005’s Push Barman To Open Old Wounds, which compiled EPs from the group’s early years on Jeepster Records. The comps function as documents of two distinct eras — one with hands in pockets, one with jazz hands ecstatically trembling.

Murdoch’s crew spent nearly two decades transitioning from neurotic, mysterious romantics to well-adjusted, heart-on-sleeve romantics. Now that transition feels complete, which makes me wonder if they have a third act in mind. Where will they take their sound next, if anywhere at all? And if they decide to keep running in place — figuratively in the band’s case, literally in Murdoch’s case — would that be a gesture of reassurance or surrender?

The Belle & Sebastian of yore is dissected at length in Pitchfork’s recent documentary about 1996 landmark If You’re Feeling Sinister, the album that still defines the band in many fans’ minds and ground zero for any inquisitor. Back then, they were geeks and spinsters spinning humble indie-pop songs as fragile as they were beautiful, populated by social caterpillars that defined mumblecore before mumblecore was a thing. Those early recordings are unpolished and clumsy, but they rumble along with unmistakable grace. This was a band on a hot streak; look no further than the first disc of the Barman comp for proof of just how deep that early catalog goes.

In those days, B&S cultivated an air of mystery, refusing to release singles from their LPs, do interviews, or even appear in promo photos. Instead, the group propagated a fantasy: “I liked the idea that it was this hipster couple in Glasgow that were making this music, like a fictional couple,” Murdoch told director R.J. Bentler. Some of that might have been brilliant strategy from Murdoch; as guitarist Stevie Jackson asserts repeatedly in the movie, “Stuart knew what he was doing.” Mystery has long been one of the most powerful tools at a musician’s disposal, particularly when musicians look as ordinary as Belle & Sebastian, and the kind of wallflowers that fell in love with Belle & Sebastian were nothing if not imaginative. On the other hand, to borrow a phrase from Glasgow band buddies Arab Strap, Murdoch and company were shy retirers, too. One surmises there’s some truth behind Jackson’s line from the 1998 B&S classic “This Is Just a Modern Rock Song”: “Stuart’s stayin’ in, and he thinks it’s a sin/ That he has to leave the house at all.”

In that context, it’s still kind of a shock to see Murdoch traipsing around stage like Freddie Mercury: a man who made a fortune selling loneliness and frustration, now apparently liberated and overjoyed. That didn’t happen overnight. Belle & Sebastian’s metamorphosis was more a gradual evolution than a clean break, even if for a while it seemed like nature might choose against them. The (ill-advised) move toward multiple songwriters and lead vocalists on The Boy With the Arab Strap and Fold Your Hands Child, You Walk Like a Peasant shepherded new sounds into a once-singular vision. Moments on Barman’s second disc, particularly the material from 2000’s “Legal Man” single, reveal glimmers of the Up With People sunshine that the band eventually basked in full-time. In 2002, Murdoch even came out of the shadows to connect with fans through his whimsical online diary. (Of course he called it a diary.) His entries from 2002-2006 were later collected into a book called The Celestial Cafe.

That said, 2003’s Dear Catastrophe Waitress, the band’s first album for Rough Trade and first produced by art-pop provocateur Trevor Horn, is a clear line of demarcation: Out with the folksy pastorals about “S&M and Bible studies,” in with the Technicolor tales of workplace seduction, lightweight Thin Lizzy guitars, and Broadway spirituals. Even then, Murdoch hadn’t yet fully embraced his current role as a human pogo stick, and tracks like “Wrapped Up In Books” showed vestiges of the old sound. On balance, though, Catastrophe was a revitalizing fresh start for a band that had squandered most of its early goodwill.

No wonder, then, that B&S followed that thread straight through its second decade as encapsulated on the new Third Eye comp. The 19-track set runs the gamut of cheery, outgoing pop, from punchy New Wave to breezy tango to radical remixes that reimagine Belle & Sebastian in the image of Annie and Animal Collective. Again, it’s not like Belle & Sebastian never toyed with electronic pop in the ’90s — one of 1995 debut Tigermilk’s best songs is the aptly titled “Electronic Renaissance” — but the latter-day tracks are slick, smooth, hi-fi. They’re professional.

So it went with Belle & Sebastian’s new world order. Old-school fans can wring their callous-free hands over it, but it was bound to happen. Even Murdoch’s heroes Morrissey and Lou Reed gussied up their sounds eventually; you can only play so long before you start to get a handle on your instrument, and a songwriter can only work in the same mold for so long before going stale. Thing is, at this point the newfangled Belle & Sebastian is as played-out as the original model. The B&S bubblegum brigade has run its course, and unless the timing of this new comp is pure coincidence, the band seems to realize that. The Third Eye Centre bookends B&S’s second era the way Push Barman To Open Old Wounds capped off the first one.

So: Where do they go from here? The way I see it, they have three options: (1) They could keep making records like 2010’s Write About Love, which, no thanks. Those ideas are bled dry. Note to Belle & Sebastian: Please don’t do this. (2) They could reinvent themselves, clearly delineating a bold new phase like Dear Catastrophe Waitress did. It’s an intriguing prospect worth exploring below. (3) They could reclaim the bookish indie-pop of Tigermilk and If You’re Feeling Sinister. Think about it: Enough time has passed that a return to the signature sound wouldn’t read as regression so much as discovering a favorite old sweater buried in the recesses of the closet. That sound would strike a deep chord with anyone invested in this band. If those Superchunk comeback albums are any indication, people would lose. Their. Shit.

I wouldn’t blame Belle & Sebastian for avoiding that path, if only because no artist should be forced to unwillingly retrace steps. Such a move implies a band understands its strengths, but also maybe is out of ideas. Also, it’s worth considering whether a return to the old sound would necessarily recapture the magic, especially now that the veil is lifted. It couldn’t be mere fan service; they would have to be fully invested and inspired to pull it off — you know, like Superchunk. But if they’re not going to revisit the past, they should forge into the future. The door seems open for the most radical reinvention of B&S’s career, should they so choose.

According to a recent interview with Under The Radar, work on the next LP is set to commence this fall. References to disco and “daddy songs” are bandied about half-seriously. Either of those routes would be a promising departure. Murdoch’s point of view has never accounted for the gargantuan responsibility of child-rearing (he just had a kid), and if there’s one prior stylistic detour the band could afford to explore further, it’s the proggy disco pop of “Your Cover’s Blown.” If they’re going to go that direction, why not a full-on disco-pop opera? After all, Murdoch has been working on a movie. Or if they really want to play against type, they could take an aggro turn and drown Murdoch’s fey storytelling in swaths of noise and distortion, exploring a side of their beloved Velvet Underground that they’ve never touched.

Perhaps those ideas are too predictable. Wherever Belle & Sebastian follows its muse, I hope it’s somewhere wonderfully unexpected. Exploring new territory this late in a career is risky — speaking of Lou Reed, anyone up for some Lulu? — but it seems like the best case scenario here: one of music’s most beloved cult favorites finding a third wind. Maybe, just maybe, they’ve got something left to give? On the other hand, if that set last month in Chicago is any indicator, they could get by just fine as a legacy act, content to retrace their greatest hits in perpetuity. A band that always romanticized the past has stacked up enough classics to feed on its own nostalgia. If they’re not interested in reinvention, though, I hope they gravitate toward the sounds that entranced so many of us in the first place rather than skirting dangerously close to showtunes parody. If we all went back to another time, I would love them over.

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The Third Eye Centre is out tomorrow, 8/27, via Matador.