But even among a collective that has made oversaturation a default mode and then continued to pile on — more appearances, more cars, more jewelry, more music — Offset has pushed excess and impulsiveness to the extreme, and emerged recently as the trio’s most compelling individual character. Last September, after a brief and turbulent courtship, he merged his life and brand with Cardi’s, marrying the platinum-selling rapper in a low-key secret ceremony (before proposing publicly at a concert the next month). Their daughter, Kulture, is his fourth child by a fourth woman.

With a new family nucleus and superstardom on the horizon, however, slowing down has still proved challenging. Ten days after Kulture was born in July, Offset was arrested in Georgia and hit with felony charges, including possession of a firearm by a convicted felon, after police discovered three handguns, some marijuana and about $100,000 in cash in his car during a traffic stop. He performed the entire Drake tour while out on bond.

At the same time, the rapper — real name Kiari Kendrell Cephus — earned three Top 15 hits without his groupmates this year, including standout verses on ubiquitous club records like Tyga’s “Taste” and Kodak Black’s “Zeze.” On Dec. 14, Offset’s 27th birthday, he will complete the Migos solo trilogy by releasing his debut album, executive produced by Metro Boomin. And while the preceding releases from the others, Quavo and Takeoff, have demonstrated the ephemerality of the modern music deluge, largely fading from the public consciousness after streaming and charting well in their opening weeks, Offset is betting on a breakout moment because he has added an element seen only in flashes throughout the expansive Migos oeuvre: introspection.

“A lot of people don’t really know Offset,” he said, because of the group structure and the flashy blog headlines about his various legal and romantic troubles. He allowed that his face, which has a panther-like intensity, is frequently in a scowl and covered in tattoos, making him “a little intimidating.” But he stressed his sense of humor, his obsession with music industry data-watching and his dedication to his mother, stepfather, friends, siblings and children, many of whom surround him at all times.

“When people talk to me, they’re like, ‘Damn, bro’ — and they don’t even notice that I notice them saying, ‘You ain’t no ignorant [expletive],’” he said. “I like that. I’m going to start opening up more.”