With the exception of the psychedelic misadventure “Their Satanic Majesties Request,” the Rolling Stones’ “Goats Head Soup” is probably the most maligned album of the group’s first 20 years. Released in 1973, it arrived as most of the bandmembers were entering their 30s and the group was entering its second decade (unheard-of for a rock band at the time), and it found them moving awkwardly into both. This fancy reissue presents a nicely remastered version of the original album, along with an album’s worth of rather forgettable outtakes, the requisite gorgeous and exhaustively researched book, and — best of all — an absolutely spectacular 1973 concert that has long been available on bootleg but here is remastered and re-whatever’ed so beautifully that it’s practically worth the price of the package on its own.

Nearly a half-century after its release, “Goats Head Soup” remains a very different kind of Stones album. It spawned what may be the first-ever power ballad, “Angie,” a string-drenched sob-fest that was a worldwide smash but alienated fans jarred by the sentimentality coming from the definitive rock and roll bad boys. It found the group at a new peak of success but seemingly insecure about where to go next, with their supremacy challenged by the gargantuan Led Zeppelin on one side and glam-era newcomers like David Bowie, Elton John and T. Rex on the other. (In a sort of competitive-adaptation strategy that Mick Jagger has employed throughout his entire career, he tried to place himself both above and within the new breed, palling around with Bowie and wearing an almost comical amount of makeup.) And it ended the group’s near-peerless streak of albums that began with “Beggars Banquet” in 1968 and ran through “Let It Bleed” and “Sticky Fingers” to “Exile on Main Street.”

Yet the biggest change agent was Keith Richards’ heroin addiction and his voluminous ensuing legal troubles, which found him abdicating to Jagger his role as the band’s musical heart and mind. Even though the songs are credited to Jagger-Richards, the primary musical foils here are lead guitarist Mick Taylor (who Jagger has hinted is the actual cowriter of several songs) and keyboardists Nicky Hopkins (who shines on “Angie”) and Billy Preston, an outsized personality who’d played with everyone from Little Richard to the Beatles, and brought a funk element that marked another stylistic change for the band. Light on riffs and the Gram Parsons-ish country vibe that marked its predecessors, “Goats Head Soup” may have less Keith Richards than any other Stones album — he doesn’t even play guitar on three of its 10 songs.

None of which is to say that it’s not a good album — it is, and finds the group exploring rare or new terrain. Keith gets his licks in on the Chuck Berry-ish “Silver Train” and “Star Star” (a groupie ode originally titled “Starf—er”), and the opener “Dancing With Mr. D” features one of his most indelibly simple riffs. “Winter” and the unsubtly titled Richards-sung “Coming Down Again” show a gentler side, and the trippy “Can You Hear the Music” revisits the exotica of “Satanic Majesties.” “100 Years Ago” and particularly “Heartbreaker,” Jagger’s stab at a Temptations-style inner-city lament, place Preston’s funked-up clavinet to the fore.

As for the outtakes, the group’s relatively low productivity during these sessions did not leave boxed-set compilers much to work with — the two key unfinished tracks, “Waiting on a Friend” and “Tops,” were dusted off and gussied up for 1981’s “Tattoo You” (which was basically an outtakes collection masquerading as a new album). And even Jagger recently said the “Goats Head Soup” outtakes were “terrible,” although he dialed that back to “not finished.”

He’s not wrong: While “Scarlet” is an intermittently fascinating song featuring Led Zeppelin’s Jimmy Page on lead guitar, it’s obviously just a run-through; “Criss Cross” and “All the Rage” are also half-baked. (It’s unclear why the country-flavored “Through the Lonely Nights,” which was recorded for this album but released a year later as the B-side of “It’s Only Rock and Roll,” isn’t included.) There are also a few alternate mixes, instrumentals and a piano demo of “100 Years Ago.”

However, the real prize here is a pristine recording of a 1973 concert that has been available for decades as the “Brussels Affair” bootleg, and was even officially released on the group’s website a few years ago — it’s long been considered one of the group’s very best live recordings, and justifiably so. Recorded toward the end of that tour, the group (accompanied by Preston and a horn section) is in top form, charging through 11 songs from the “Beggars”-“Bleed”-“Sticky”-“Exile” quartet of albums and four from “Goats Head Soup” — “Dancing With Mr. D” is particularly hot and crushes the album version. While the Jagger-Richards-Charlie Watts core is in peak form, the two quiet members — Mick Taylor and bassist Bill Wyman — also put in dazzling performances. This was one of Taylor’s last concerts as a Rolling Stone (he left the following year), and while his increasingly jazzy style had begun to diverge from the band’s rock-hard basics, he peels off one quicksilver solo after another. Likewise, the eternally underrated Wyman underpins the songs with some understated soloing of his own — usually buried in the mix on the studio albums, his octave leaps and zooming runs add a subtle dimension to the sound (no matter what one thinks of his hideous bragging about his even more hideous womanizing, he remains one of rock’s greatest bassists). It’s absolutely glorious.

“Goats Head Soup” marks the beginning of a minor identity crisis for the Stones, one that would continue for the next two albums, “It’s Only Rock and Roll” and “Black and Blue.” However, when Ron Wood replaced Taylor in 1975, his enthusiasm and Richards-esque playing brought the group back to its essence — and decades later, they haven’t looked back.