Young men are staggering around, hungry for days. They are throwing themselves into ice baths and cryotherapy pods. There are not enough beds at the silent vegan meditation centers to accommodate them. They need more near-infrared bulbs.

They are the followers of Jack Dorsey, Silicon Valley’s answer to the mega-influencer Gwyneth Paltrow. The lithe, 42-year-old tech founder has become a one-man Goop.

“In terms of influence, no one is at the scale of Jack,” said Geoffrey Woo, whose start-up, HVMN, sells fasting tools (like a liquid ketone supplement). He also heads up WeFast, an online support network for intermittent fasters.

It’s unlikely that Mr. Dorsey can embrace his wellness guru role as fully as Ms. Paltrow. He is already the chief executive of both the payments platform Square (valued at $30 billion) and Twitter (valued at $26 billion). As Twitter’s head, he spends his days navigating issues around free speech for white supremacists, online abuse and the spread of terrorist propaganda, all while facing a deluge of criticism from everyone (including the American president).