Pleased to Meet Me was the sound of the Replacements trying for once. The band’s previous five LPs were snarky slacker masterpieces full of chintzy songs about hating music ’cause it’s got too many notes, ironic Kiss covers, and the occasional tender ballad, and their concerts were more like drunken hootenannies — all of this sloppiness was what won them their legend. But sometime after recording their beloved Tim album, Paul Westerberg decided they ought to grow up a little, the group parted ways with founding guitarist Bob Stinson, and the ‘Mats became self-aware.

They lost some of their danger, recording the very produced LP as a trio with a supporting cast of thousands, yet still managed to cough up two all-time classics — the beat-skipping “Alex Chilton” on which you can hear Westerberg exuberantly catching his breath and the mellow love letter “Can’t Hardly Wait.” They also recorded a handful of almost classics (“Skyway,” “IOU”), and some tongue-in-cheek head scratchers (the faux-jazzy “Nightclub Jitters” and what might be the Replacements band diary, “I Don’t Know”). In spite of some über-Eighties, ultra-reverberated production (which still sounds better than their next album, Don’t Tell a Soul), the record was the band’s last moment of greatness.

This new box set shows how the album could have been even better. The Replacements recorded a lot of music around Pleased to Meet Me, much of which came out on various singles and compilations, as well as demos, alternate versions of songs, and tunes that for whatever reason were forgotten in the back of the beer fridge.

The most interesting stuff here is in the Blackberry Way Demos, some of which came out on a previous expanded edition of the album. Eight of the tracks feature some of Stinson’s last recordings with the band, and his whiplash snarls on “I.O.U.,” rockabilly shredding “Time Is Killing Us,” and tasteful accents on “Valentine” show what the album could have been. These recordings all have a raw, intimate quality that sounded polished on the LP. Even the demos they cut as a three-piece show how playful they could be; the two versions of Westerberg’s anti-TV screed “Kick It In” demonstrate how they could give a song a facelift on a whim, playing it straight on the first demo and adding bongos and more guitar textures to the second. And the country-rocking “Even If It’s Cheap” is a nice addition, if only to hear Tommy Stinson sing the album title: “Pleased to meet me, the pleasure’s all mine, I’ve seen you here before.” The winking nature of the way he sings the verse and the bridge that sounds a bit like “Jesse’s Girl” maybe explain why it didn’t make it much farther.

Even the collection’s rough mixes — usually the most over larded part of a box set — offer new insights. Gospel organ ran through the original mix of “Valentine.” It sounds like somebody played a little mandolin in “Alex Chilton” at some point. And the strings on the original “Can’t Hardly Wait” stepped on the dropout when Westerberg sings the title.

Of the three fully mixed, never-before-released tunes, “Learn How to Fail,” is the best with its jazzy guitar line and Westerberg convincing someone young to grow up a little before they start dating, followed closely by Tommy Stinson’s hard-rocking “Trouble on the Way.” “Run for the Country,” which features some harmonica, feels a little schmaltzy, and the previously unreleased cover of Billy Swan’s “I Can Help” pales in comparison with the raving drunk cover of the same tune they cut with Tom Waits (on last year’s Don’t Tell a Soul box set).

Taken as a whole — along with Replacements’ biographer Bob Mehr’s ever-excellent liner notes (which shed some light on Bob Stinson’s departure) — the holistic skyway-view of the album shows a band that was a little looser than they would want to let on. The ache in Westerberg’s voice feels deeper on several of the songs, and the way the group could settle into a jam, whether as a four-or three–piece, sounds easier. Now you can finally hear how they tried and where they succeeded.