Several band members disagreed with Dammers' vision and brought their own influences to the album, including from northern soul and rockabilly, contributing to an eclectic sound palette.

The album features collaborations with the Go-Go's members Belinda Carlisle, Charlotte Caffey, and Jane Wiedlin; Rhoda Dakar from the Bodysnatchers; and Lee Thompson from Madness.

Formed in Coventry in 1977, the Specials were the originators of 2 Tone music, a style that mixed the Jamaican genres of ska and reggae with the attitude and energy of punk rock and a focus on politically and socially conscious lyrics.

The subsequent debut album The Specials (1979) was a critical and commercial success, while the Too Much Too Young EP released in early 1980 reached number one in the UK Singles Chart.

"[2] A new single was required, so the band released "Rat Race", written by guitarist Roddy Byers as a critique on how privileged students "would spend three years pissing it up in college, knowing full well that Daddy would get them a good job when they left no matter what.

"[2] With Linton Kwesi Johnson's "Me Wan' Fi Go Rave" as a musical starting point, band founder and keyboardist Jerry Dammers added a plucked piano intro inspired by John Barry, foreshadowing his primary direction on More Specials.

His ambition with More Specials was to destroy people's preconceived ideas of good and bad music to the point where listeners would hear a record and "won't even know if they like it or not."

[11] The guitarist stated he wanted to start his own band to play his rockabilly-styled rock and roll, which would have been stylistically consistent with acts like Stray Cats who were becoming popular in London.

[12] Consequently, he had begun creating songs in punk rock and power pop styles,[10] while Bradbury's interest in northern soul remained intact, thus contributing to the varied sound of the final album.

[2] Recording was also hindered by outside interference, including when a journalist entered the studio to interview the band, who felt the interruption had sabotaged the "vibe" of the song they were working on.

For the Muzak-style tracks, including "Stereotypes", "I Can't Stand It" and "International Jet Set", the band sacrificed the live 'ensemble' recording of their first album for a "one instrument at a time" multitrack recording style, firstly laying down the keyboard and drum tracks, then adding bass, then guitar, and so on, contributing to a "totally different feel to the music" that Panter disliked.

[20] Contrasting the often upbeat music, the record's lyrics are comparably bleak, depicting English life "in all its drab, suffocating despair and there's no way out," according to Nick Reynolds.

[13] John Lewis of Uncut wrote that, compared to the "teenage male fear writ large" on the band's first album, More Specials "presents a dread that’s more existential than adolescent.

"[13] In the version that opens the album, the song is upbeat, with inventive drumming from Bradbury,[21] but ironically hints at the nation's then-fear of a potentially impending nuclear war.

[5] Indicating the band's move away from ska, the song's horn arrangements are said by Goldman to "evoke Bernard Herrmann and the Northern Dance Orchestra more than the cool jerk at Studio One.

"[21] "Man at C&A", Hall's first composition, also shares a theme of nuclear war with its lyrics addressing doomsday, and was described by Simon Reynolds as a "film soundtrack/Muzak fusion.

[23] Lee Thompson of Madness contributes saxophone solos to "Hey, Little Rich Girl",[24] which concerns an aspiring young woman whose career detours into pornography after moving to London.

[24] Peter Chick of The Guardian noted that "[t]he track might conjure a blissful, muzak-smooth, easy-listening utopia, but – as seemed to be More Specials' bleak theme – underneath the surface, everything was fucked up.

[15] "Holiday Fortnight" is an instrumental flavoured by Mexican and calypso music,[23][24] whereas "I Can't Stand It" contains cool jazz licks,[21] and was one of the first songs Dammers had ever written.

[15] "International Jet Set" is a bleak psychedelic track in an exotica and "elevator music" style with a sitar-style groove and lucid synths.

[5][15][22] Lyrically, Hall narrates a personal nervous breakdown on a McDonnell Douglas DC-10 aeroplane in which he talks of the misery of life and his alienation, before the sound of a captain announcing over the PA that the plane is to take a crash landing, presumably killing its passengers.

[21] With photography from Carol Starr and Chalkie Davies,[8] the album cover of More Specials depicts a "cheesy" out-of-focus colour photograph of the band snapped in the bar of the former Regent Hotel in Leamington Spa.

[28] In September 1980, the first single from the album, a double A-side of "Stereotypes" and "International Jet Set", was released to present the band's new "post-ska" sound.

[1] Critical reception to More Specials was very favourable, with Vivien Goldman of the NME, John Orme of Melody Maker, Mike Gardner of Record Mirror and Garry Bushell of Sounds all praising the album and considering it a bold step for the band.

"[47] In the NME, Goldman felt that "[f]ans expecting more frenetic ska re-runs will do a treble-flip when they hear the conglomerate of Zhivago-esque movie soundtracks and other much-maligned musics the Specials have re-validated.

"[21] In Smash Hits, David Hepworth felt the decision the change in direction was wise and called the record "[a]n original and highly intelligent album that suggests The Specials can keep it up if you can.

"[48] In his Record Guide, Robert Christgau was somewhat less receptive, saying that although "they make the ska sound their own by synthesizing its trippy beat and their own inborn vocal attenuation into a single formal principle--a platonic ideal of fun," this becomes so conspicuous on side two that "the result is so light it's almost ethereal, political consciousness and all.

"[38] Among retrospective reviews, Jo-Ann Greene of AllMusic reflected that the album was "an intensely satisfying set in its day, even if it wasn't as centered as their debut.

"[24] In Uncut, John Lewis complimented the lyrical "dread that's more existential than adolescent," but felt "the most interesting development is the sonic shift from monochrome into Technicolor.

[19] Wade also cites the B-sides "Supa Shoppa" (1994) and especially "The Horrors" (1995) as further examples, the latter song combining "a cheap tango rhythm-preset with schoolhouse piano to push More Specials' postcard bleakness into something approaching existential dread.