How do you follow a cultural phenomenon like “Succession”? If you’re Jesse Armstrong, it doesn’t hurt to build on what you do best: making fun of childish billionaires on HBO.

Armstrong returns to the premium cable network in May with “Mountainhead,” an HBO original movie he wrote and directed with a premise that could be ripped right out of “Succession.” The film follows four tech moguls with a combined net worth of nearly $400 billion who meet in an alpine mansion for a weekend of skiing and poker. But their bros’ getaway is soon derailed when they find themselves fighting over a global meltdown that may or may not be caused — or at the very least, amplified and expedited — by their own social media platforms.

Additional cast members for “Mountainhead” include Hadley Robinson, Andy Daly, Ali Kinkade, Daniel Oreskes, David Thompson, Amie MacKenzie, and Ava Kostia. The film is executive produced by Armstrong,...