By now, the formula for blown-out editions of landmark albums is set in archival stone. For your extra dollars, you’re handed an updated, sonically enhanced version of the original album, a smattering of alternate takes of its songs, maybe a few tracks that had been relegated to the vaults or a DVD with period footage. The boxes complement, rather than upend, the core record.

But in multiple beguiling ways, the 50th anniversary revisit of Crosby, Stills, Nash & Young’s Déjà Vu  offers up a new twist. Released in time for its 51st birthday (these guys always broke the rules, starting with the use of their names as a band), it asks you to imagine the ways in which one of the more beloved classic-rock albums could have been almost entirely unlike the album we’ve known since 1970.

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For their first full-on studio collaboration with Neil Young on board, CSNY headed into Déjà vu in the summer of 1969 in various states of psychic fragility, cockiness, and apprehension. The album that emerged from the charged and often fraught sessions largely lacked the sunshine-harmony joy of its predecessor, Crosby, Stills & Nash. From the wail-of-sound harmonies on their rocked-out cover of Joni Mitchell’s “Woodstock” to the living-room warmth of Graham Nash’s “Our House,” it had moments of brightness. But a sense of tension and terseness ran throughout most of its 10 songs — the perfectly timed soundtrack for an increasingly discombobulated generation grappling with life during Vietnam, Richard Nixon, and everything else hitting them at once.

But these four men, either at or approaching their creative peaks, also arrived with piles of new material, and this four-disc set attempts to bring order to it all. The first disco offers up the expected shiny new mix of Déjà vu;  the sonic freshening-up is clearly felt on tracks like the closing “Everybody I Love You,” where the instruments sound punchier and crisper.

A separate disc offers up the same song-by-song lineup (save for Young’s “Country Girl” suite) but in alternate mixes or outtake versions — the bizarro-world version of Déjà vu. That means we hear Stills’ stampeding opener “Carry On” with a few guitar lines excised at some point; a folksier “Teach Your Children” without Jerry Garcia’s pedal steel; or “Woodstock” with a less urgent Stephen Stills vocal but jauntier piano. David Crosby’s “Déjà vu” sports more homogenized harmonies that lack the ghostly beauty of those on the released take, but this “Our House” actually feels a tad more forceful in its delivery and piano. None of these replacement takes is markedly different than the versions we know, save “Almost Cut My Hair”: here, Crosby’s voice doesn’t quite have the raspy attack of the released take and Stills and Young’s guitar-solo lobbing feels a little messier and more embryonic. But even that track adds another piece to the CSNY puzzle: the sound of these four (sometimes three) men at work in a studio, something we’ve rarely heard save for random bootlegs.

The remaining discs constitute largely solo, acoustic demos of songs under consideration (disc two) or nearly completely full recordings that didn’t make the cut (disc three). Here’s where things get far more interesting. CSNY archivists will enjoy the alternate take of Stills’ “4 +20” without the slight gulp in his voice on the final verse, or an “Our House” with Nash’s then-partner, Joni Mitchell, chiming in and also laughing when Nash screws up the lyric. But these discs also give us a sense of how altered in mood and sequencing Déjà vu could have been — in essence, it could have been their own sprawling White Album, and perhaps all the better for it.

For instance, the box imagines what Déjà vu would have been like had it included Crosby’s “Laughing,” his take on George Harrison’s spiritualism, heard here in a not fully developed group version. It’s not as eerily beautiful as the one Crosby would do on If I Could Only Remember My Name, but it’s easy to imagine it fitting in with the album. The idea that so many quality songs — Stills’ lovelorn “So Begins the Task” (one of his most vulnerable and beautiful of the era) and “Change Partners” (the latter in an electric take) and Crosby’s “The Lee Shore” (with, again, the band playing along)  — didn’t make the cut is, in retrospect, pretty staggering. Déjà vu would have also been a more delicate, more inward album had it included Crosby’s wordless beauty “Song with no Words (Tree with No Leaves),” included here as a demo with Nash, or Young’s “Birds,” featuring Nash’s whistly harmony. And what they also left off were the outright pop songs: Stills’ semi-autobiographical “Same Old Song” and Nash and Terry Reid’s “Horses Through a Rainstorm” would have made Déjà vu a shade less cloudy.

On the matter of Young, his presence on this archival dig is frustratingly minimal. From all reports, Young was in and out of the sessions to begin with, but over the years, a few of his contributions, like a bubbly group version of “Everybody’s Alone,” have made their way onto bootlegs. As Nash confirmed to RS recently, though, Young decided to yank some of his Déjà vu leftovers at the last minute. Other than “Birds,” his only vault addition here is a version of “Helpless” with harmonica, but that’s been available on the first volume of Young’s own archival box for years, and is now on the Neil Young Archives site. Could we at least have heard one of the rumored alternate versions of “Helpless” before the band’s playing slowed down enough to suit Young? The omissions are unfortunate — another missed group opportunity in a saga filled with them.

Just as Young’s spectral presence on this set reminds you of his own noncommittal arrangement with the band, the outtakes disc also harks back to the period when Stills was both driven and the head driver of CSNY. On that disc, eight of the 11 songs are his, and he’s clearly on fire. Stills pounds out a credible Motown vibe for the autobiographical “Same Old Song”  and introduces his first pass at a slower, pained revamping of his Buffalo Springfield opus “Bluebird,” as “Bluebird Revisited” (he eventually redid it again for a solo record). Even when the songs don’t sound fully formed, as on the vampy yowl of “Right on Rock ‘N’ Roll,” the conquer-the-world energy he brings to them, combined with a voice not yet ravaged by time and abuse, is a startling reminder of his capabilities at the time: You can feel the music bursting out of him, no matter where it would go.

Most of that disc amounts to an unheard Stills solo album, and the seeds of some of his later solo cuts, like “Church (Part of Someone)” and “Sugar Babe,” are planted here in, respectively, “She Can’t Handle It” and “Ivory Tower.” A few of the other rejects feel personal too; Nash’s “Sleep Song” and Crosby’s ménage à trois “Triad” feel ready-made for individual projects, not group arrangements. But those moments are equally telling. The original Déjà vu presented CSNY as a united front even as the group was already fraying. This excavation tells the other part of the story: four men working together and, at the same time, starting to drift into their own separate, occasionally colliding worlds.

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