Bridgespan itself received a gift from Ms. Scott. Bridgespan’s latest tax filing for the year 2020 showed contributions and grants leaping to $74.7 million from $12.5 million the year before, nearly doubling the group’s total assets as of the end of last year. Bridgespan said the increase reflected a five-year capital campaign with multiple donors and not just Ms. Scott’s grant.

Giving away money used to be approached as a distinct enterprise from making money. The strategies, language and reams of analytics do not always translate to the nonprofit world, where “return on investment” could be harder to quantify.

“We were getting into bidding wars. ‘I can serve 500 kids for a million dollars.’ ‘I can serve 500 kids for $400,000,’” said Geoffrey Canada, president of Harlem Children’s Zone and one of Bridgespan’s first clients. He said he found his initial encounter with the group “predictably demeaning — they come in, lay out charts, don’t give you the chance to answer back.”

What was different from other firms his nonprofit worked with, he said, was Bridgespan took his “brutally honest” feedback to heart. In turn, they persuaded him to abandon the bidding wars and ask for more money, trusting the donors to respect his candor.

Attitudes toward billionaire philanthropy shifted after the Great Recession, with populists on the left and right more suspicious of the ultrawealthy. Yet management consulting for philanthropists and nonprofits continued to thrive. That is partly because the pie keeps growing.

From 2000 to 2018, assets held by private foundations more than doubled, according to the research group Candid, to $950 billion from $421 billion. Total giving tripled over the same period, the most recent for which complete data is available, rising to $72 billion from $23 billion, according to Candid, which also received a grant from Ms. Scott.

Instead of establishing big foundations, many of the richest Americans now want to use limited-liability companies, like Laurene Powell-Jobs, and donor-advised funds, which Ms. Scott has used for some of her gifts.

“Bridgespan seems exceptionally able and well-disposed to take advantage of the shift from big family foundations to L.L.C.s that don’t want staff but are still giving away a huge sum of money,” said Rob Reich, co-director of the Center on Philanthropy and Civil Society at Stanford University.

Groups like Bridgespan can also step into the gap and serve as outsourced staff for new foundations finding their footing.

In March, the recently formed Asian American Foundation had just five full-time employees. After the killing of eight people at Atlanta-area spas, six of Asian descent, the group was inundated with pledges and commitments, including millions more from prominent board members including Joseph Tsai, owner of the Brooklyn Nets, and a further $1 billion committed to their cause by foundations, corporations and individuals in an eight-week period.

Mr. Hussein of Bridgespan served as an informal adviser, joining calls with board members.

The foundation brought on a team from Bridgespan full time over the summer. “My ask of them was understanding what is happening in the field and what are things we should be paying attention to. Where were the gaps?” said Sonal Shah, the foundation’s president. The Bridgespan team provided a thorough analysis of Asian American and Pacific Islander organizations in the United States.

“I think it was over a four-week period, which is not a small thing to do in a month,” Ms. Shah said.

Ms. Shah said she appreciated the fact that the team from Bridgespan was staffed fully with people of Asian descent. Mr. Hussein said that was intentional. He drew from Bridgespan’s internal affinity group, people with “firsthand experience of what it means to be othered, what it means to have the model minority myth,” Mr. Hussein said.

That was not the case in the group’s early days, said Mr. Walker, of the Ford Foundation.

“When I first met Bridgespan, it was primarily white men at the top and that’s not a surprise given their origin,” Mr. Walker said. “I had a Zoom call with the Bridgespan team on a matter last spring and a majority of the people on the little Hollywood Squares on the Zoom were people of color and women.”

Bridgespan’s self-reported diversity figures show two-thirds of the group’s staff are women. White people make up less than half of the overall staff, as well as less than half of those in leadership positions.

Both Mr. Walker and Jeff Bradach, one of Bridgespan’s founders, used the word “journey” to describe the group’s embrace of diversity and inclusion as central tenets of the work. Mr. Bradach, who was managing partner until October, when he stepped down from the top post, stressed in an interview that this was still a work in progress and that Bridgespan had made mistakes in the past.

For instance, one of Bridgespan’s big pushes was for donors to make “big bets” rather than spreading the money around. But that standard tends to favor big institutions. “If in your criteria, you say, ‘We only fund people that do random control trials,’ if you have these barriers to capital on general operating support, then a whole bunch of organizations led by people of color have actually never been given the money to do that,” Mr. Bradach said.

Ms. Scott has made it a priority to give to such previously underfunded groups. But she has no website or headquarters or way to apply for grants, leaving groups scrambling for a way to get on her radar. People in the field noticed, for instance, that Bridgespan has advised the YMCA and Ms. Scott gave grants to YMCA’s across the country last year.

While avoiding directly discussing Ms. Scott’s giving per company policy, Mr. Bradach rejected the notion that nonprofits could work with Bridgespan as a way of getting the attention of the big donors they advise. Mr. Bradach said that just 5 percent of the nonprofits that Bridgespan’s philanthropic clients gave to were also Bridgespan clients.

In that 5 percent of cases, Bridgespan policy is to tell the donor that it also represents the nonprofit. The notion among nonprofits that they could cozy up to Bridgespan and then receive huge sums from Ms. Scott is wrong, Mr. Bradach said, and also betrays a misunderstanding of how much sway Bridgespan has over the donors who seek its help. “It’s not,” he said, “a black box that they’re kind of scratching their head going, ‘I can’t wait to see what comes.’”