For the early punks, many of them white British blokes, their music was about declaring themselves outside the larger society. The Sex Pistols dreamed of “anarchy for the U.K.” The Clash howled for “a riot of my own.” To be punk was to give offense, to make one’s self unpalatable, to choose to stand apart.

But what is punk when your society has already made you an outsider? This is the musical question that the raucous, cheeky comedy “We Are Lady Parts,” returning Thursday for its second season on Peacock, seeks to answer.

The first season, back in 2021, introduced Lady Parts, a punk band of Muslim women in London: Saira (Sarah Kameela Impey), the caustic lead singer; Ayesha (Juliette Motamed), the fearsome drummer; and Bisma (Faith Omole), the earth-motherly bassist. Together with their manager, Momtaz (Lucie Shorthouse), a savvy Malcolm McLaren in a niqab, they recruit a reluctant lead guitarist, Amina (Anjana Vasan).

Amina is no one’s idea of a rock star, least of all her own. She is an introverted microbiologist who worships Don McLean, with a severe case of stage fright that causes her to heave her guts while performing — and not in a defiant, Iggy Pop way. (Vasan gives Amina an engaging nerd-hero energy, similar to Quinta Brunson in “Abbott Elementary.”)

Over the six-episode season, Amina finds that Lady Parts gives her a way of defining herself rather than being defined, whether by the conservative suitors who tell her “Music is haram” or by her free-spirited mother (Shobu Kapoor), who wishes Amina would wait to seek a husband.

The root conflicts of “We Are Lady Parts” are familiar rock-band woes — having no money, having no gigs, being judged by family and by hipsters. This is where making the series about Muslim women rockers accomplishes more than representational box-ticking: It makes an old story new and nuanced.

For Amina and the rest of the band, rebellion is complicated. It means being Muslim women musicians, with equal stress on both adjectives. (The name Lady Parts itself feels like an answer to the anatomical name of the Pistols.) It means owning their sexuality and spirituality, seizing the right to define what being Muslim means to them and affirming their Muslim identity, as reflected in their sly, effectively catchy songs (co-written by the show’s creator, Nida Manzoor).

“Voldemort Under My Headscarf” embraces the traditional garb as a badass statement as defiant as any ’70s punk’s safety pin. (“I’m sorry if I scare you/ I scare myself too.”) “Bashir With the Good Beard” addresses a certain kind of haughty, elusive boyfriend. (“Are my clothes too tight?/ Do I laugh too much?”)

The series has some resonance with the recently ended “Reservation Dogs,” though its sense of humor is more rowdy and brash. It, too, is a story about young people asserting their individuality while affirming their community rather than rejecting it. The first season’s climax, in fact, involves the band being mischaracterized by an article profile that labels them “Bad Girls of Islam.”

Season 2 finds Lady Parts in the flush of minor success. (The show also shows signs of having hit the big time, attracting guest stars including Malala Yousafzai.)

The band has finished a camper-van tour of England and is planning an album. Their fan base now includes not just Muslim kids, but Muslim kids’ parents, as well as middle-aged white people, whose cringey praise recalls the garden party guests from “Get Out.” Amina has mastered her stage fright and — with occasional wobbles — is embracing her confident “villain era.”

The show’s sophomore outing is as brassy as the first, but adds layers of theme and character. Early on, the band discovers it has competition in a younger Muslim band, Second Wife. (“That’s good,” Ayesha grudgingly acknowledges of the name.) Rather than set up a battle of the bands, “We Are Lady Parts” puts a twist on the “There can only be one” mentality that pits underrepresented artists against each other.

As the band progresses, and Amina grows into her romantic confidence, the season plays with the way a kind of fetishizing adoration can be as toxic as rejection, both artistically and personally. Being stared at because of your head scarf, in post-Brexit Britain, is alienating, but so is being asked to keep your head scarf on to protect your Muslim-punk brand.

Over six episodes, the season fleshes out its supporting characters, wrestling with who they are and what they want to say. Bisma, who is married and has an adolescent daughter, starts to feel typecast as the group’s maternal figure. (“I am Mommy Spice. I am Wholesome, Boring Spice.”) Ayesha is dating a woman but is reluctant to come out to her parents, which makes her worry that she’s letting down her gay fans. Saira, the most old-school-punk of the group, itches to branch out from “funny Muslim songs” and write more pointedly political material, but that risks hurting the band commercially.

It’s hard not to see this last story as a meta-comment, intentional or not, on what the series itself can get away with saying, on a major media platform, with these characters. There is reference, for instance, to Saira wanting to speak out on how Muslims are being persecuted around the world, but less reference to any specific conflict, be it in Gaza or elsewhere.

One striking scene makes this sense of invisible boundaries literal, as Saira struggles to put her politics into song form. She runs through a verse: “It’s like death and the maiden / Dancing with my corporation / I won’t mention the w—” The what? The world? The war? We never hear. Her mouth is pixelated as she tries to finish the line, over and over; she strains and screams but the word won’t come out. Whether “Lady Parts” chooses not to complete her lyric or can’t, the image of asphyxiating silence is potent. (The episode closes with a song by the Palestinian singer Rasha Nahas.)

Of course, getting silenced by the industry is another perennial tale of rock ’n’ roll, among other vocations. As in Season 1’s getting-the-band-together arc, the challenges of making it are superficially familiar from other music stories: What is selling out? How do you distinguish growth from compromise? Can you make it big without abandoning any of your mates?

But the execution and the details are captivatingly specific. What works about “We Are Lady Parts” is what works about great punk. You can still fashion something new out of the same old three chords. You just need a distinctive voice.