While cracking the crowded American rap market will be challenging, Stormzy’s team is hopeful. “Boundaries don’t exist anymore,” said Michael Kyser, the president of black music at Atlantic Records, which is releasing the album in partnership with Stormzy’s own #Merky imprint, the label arm of his #Merky empire. “Hip-hop is a genre that brings people of all backgrounds together, and we plan on helping Stormzy continue that mission around the world, including in the U.S.”

Stormzy has shared stages with Kanye West and Ed Sheeran, yet he thrives alone. In June, he became the first black British solo artist to headline Glastonbury, the iconic British music festival founded in 1970. He filled the stage with a prismatic vision of black Britain that included boys on BMX bikes and ballet dancers, and he blasted a speech by the Labour politician David Lammy about racism and the country’s criminal justice system. He said the ambition of the set was inspired by Beyoncé’s landmark Coachella performance. Even so, he said that he has yet to peak as a showman.

“I’ve set the bar,” Stormzy said. “It gives me boundaries to soar over.”

Before the trip to his school, Stormzy was blasting West’s “The Life of Pablo” at his spacious home in a leafy area of southwest London. The record’s thick bass reverberated off the marble and chrome décor. “I wanted it to be very homely,” he said of the residence. The dozens of high-end liquor bottles lining a mirrored bar said otherwise. “But it’s ended up looking like a bit of a bachelor pad,” he added.

In truth, the workaholic Stormzy is rarely at home. He spent around two years working on “Heavy Is the Head,” which lets his musical curiosity off the leash, as grime takes a back seat to silky R&B, staccato hip-hop beats, radiant gospel and the love of pop that he broadcast with a 2014 Justin Bieber cover. Reliable hitmakers — Paul Epworth (Adele, Coldplay), Frank Dukes (Lorde, Drake), Mark “Spike” Stent (Beyoncé, Lady Gaga) — fill the credits and give the LP a dynamic gloss, in a clear sign of Stormzy’s expanding ambitions. (Weeks of sessions with Pharrell Williams, however, didn’t pan out.)

“Stormzy’s right up there with the best of people I’ve ever worked with,” said the producer Fraser T. Smith, who has collaborated with Adele and Sam Smith, and worked with Stormzy since “Gang Signs & Prayer.” “He’s brave, unapologetic and forward thinking. A true visionary.” As far as breaking through to America, Smith is unconvinced it’s a necessary goal: “Rap music is parochial, and there’s power in that.”

Stormzy’s determination to move his music beyond grime has been treated with scorn by some older M.C.s. “They want grime culture to be protected,” he said blithely, while tucking into a meal prepared by a private chef. “They don’t want the mainstream coming in and watering it down. To them I’m an annoyance; a stain.”