And efforts to insulate the foundation from potential conflicts have highlighted just how difficult it can be to disentangle the Clintons’ charity work from Mr. Clinton’s moneymaking ventures and Mrs. Clinton’s political future, according to interviews with more than two dozen former and current foundation employees, donors and advisers to the family. Nearly all of them declined to speak for attribution, citing their unwillingness to alienate the Clinton family.

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Last Thursday, Mr. Clinton arrived two hours late to an exuberant welcome at a health clinic about 60 miles north of Johannesburg. Children in zebra-striped loincloths sang as Mr. Clinton and Ms. Clinton made their entrance, and the former president enthusiastically explained how his foundation had helped the South African government negotiate large reductions in the price of drugs that halt the progress of HIV. Aaron Motsoaledi, South Africa’s minister of health, heaped praise on the effort. “Because of your help we are able to treat three and a half times more people than we used to,” he told the crowd.

The project is typical of the model pioneered by the Clinton Foundation, built around dozens of partnerships with private companies, governments, or other nonprofit groups. Instead of handing out grants, the foundation recruits donors and advises them on how best to deploy their money or resources, from helping Procter & Gamble donate advanced water-purification packets to developing countries to working with credit card companies to expand the volume of low-cost loans offered to poor inner city residents.

The foundation, which has 350 employees in 180 countries, remains largely powered by Mr. Clinton’s global celebrity and his ability to connect corporate executives, A-listers and government officials. On this month’s Africa trip, Mr. Clinton was accompanied by the actors Dakota Fanning and Jesse Eisenberg and the son of the New York City mayoral candidate John A. Catsimatidis, a longtime donor.

For most of the foundation’s existence, its leadership has been dominated by loyal veterans of the Clintons’ political lives. Ira C. Magaziner, who was a Rhodes scholar with Mr. Clinton and ran Mrs. Clinton’s failed attempt at a health care overhaul in the 1990s, is widely credited as the driving force behind the foundation’s largest project, the Clinton Health Access Initiative, which, among other efforts, negotiates bulk purchasing agreements and price discounts on lifesaving medicines.

Mr. Band, who arrived at the White House in 1995 and worked his way up to become Mr. Clinton’s closest personal aide, standing behind the president on golf courses and the global stage, helped build the foundation’s fund-raising structure. He conceived of and for many years helped run the Clinton Global Initiative, the annual conference that draws hundreds of business leaders and heads of state to New York City where attendees are pushed to make specific philanthropic commitments.

Today, big-name companies vie to buy sponsorships at prices of $250,000 and up, money that has helped subsidize the foundation’s annual operating costs. Last year, the foundation and two subsidiaries had revenues of more than $214 million.