But Mr. Harrison, who approaches his work with an entrepreneurial zeal, now wants to scale up his operations, and is aiming to reach an additional 25 million people by 2025. He hopes to raise $1 billion over the next seven years, $800 million of which would go to program costs and $200 million to back-end support for field operations, rent and payroll.

To accomplish as much, Mr. Harrison believes he will need to think less like a plodding foundation and more like a start-up.

“We’ve always fashioned the organization as a quickly scaling business that’s trying to acquire customers,” he said.

Mr. Harrison refers to donations as “revenue” and talks about key performance indicators. He is fluent in business speak and even calls himself chief executive officer, eschewing the traditional nonprofit leadership titles of executive director or president. To many of the entrepreneurs who support Charity: water, this is a big part of the appeal. He speaks their language. He’s one of them.

“Scott runs it like a company,” said Mr. Graves of Uber. “It’s not a bloated, cloudy not-for-profit.”

So far, it seems to be working. Charity: water’s work in the developing world draws favorable reviews even from those who question its fund-raising tactics.

And while many young tech millionaires and billionaires are criticized for being insufficiently generous, Mr. Harrison is drawing them off the sidelines and putting their money to work, sometimes in the field and soon in the form of employee bonuses.

“Scott and his team are trying to innovate,” said Mr. McKelvey of WeWork. “It’s an awesome exploration into the future of philanthropy.”