Should Hillary Clinton be elected president, there will be no end to the allegations that the way to get favors from her is to donate to the Clinton Foundation.

“Pay to play,” as Donald Trump charges. It’s become one of the most powerful applause lines in his presidential campaign, a way of putting some force behind his portrayal of his opponent as “Crooked Hillary.”

Some of Trump’s attacks on Clinton may have sell-by dates: Benghazi and even her email management as secretary of state happened in the past. The suggestion that she’d skew White House policy to please her family foundation’s rich donors is designed to make voters see how influence peddling could be run out of 1600 Pennsylvania Ave.

Even though there is no evidence yet that Clinton took any actions while secretary of state to help donors to the foundation her husband and daughter ran, “the issue is the perception,” said Rob Reich, a professor of political science at Stanford University and co-director of the Stanford Center on Philanthropy and Civil Society.

“The perception is that donating to the foundation is the way to gain influence,” Reich said. It’s a reason that philanthropy and partisan politics “mix like oil and water.”

The challenge for Clinton is that there are few surefire ways to blunt that perception, short of folding a charity that even Trump campaign manager Kellyanne Conway has said does some “very important work.” In 2014, the nonpartisan World Health Organization said the foundation’s affiliated Clinton Health Access Initiative was one of a handful of organizations that helped bring down the cost of AIDS drugs in poorer countries.

Analysts say that eliminating suspicions about a President Hillary Clinton’s ties to the Clinton Foundation will require a much thicker firewall than the agreement she signed when she became secretary of state in 2009. Then she said, “I will not participate personally and substantially in any particular matter involving specific parties in which the William J. Clinton Foundation (or the Clinton Global Initiative) is a party or represents a party.”

The Clinton Foundation signed a memorandum of understanding promising to disclose donors regularly. But it violated that provision on several occasions, including when it failed to report a $500,000 donation from the Algerian government in 2010.

Foundation contributors may not have received favors, but they got face time with Clinton. Emails released this month as part of a lawsuit by the conservative group Judicial Watch showed that Clinton Foundation officials were not shy about asking Clinton’s State Department for meetings with their donors.

Although the communications between Clinton Foundation and senior State Department aides didn’t violate agreements that Hillary Clinton signed, “they demonstrate a blurring of the lines between official government business and Clinton’s personal connections — breaking the firewall Clinton agreed to preserve,” the nonpartisan fact-checkers at Politifact said last week.

To tamp down what he called “legitimate concerns about potential conflicts of interest” should his wife become president, Bill Clinton said last week that the foundation would no longer accept donations from corporations and foreign governments.

And he said he would leave the board of the Bill, Hillary and Chelsea Clinton Foundation and no longer raise money for it. Hillary Clinton, who had returned to the board after resigning as secretary of state, left it again when she announced her run for president last year. But Chelsea Clinton intends to remain with the foundation, making her father’s promised departure all but meaningless in skeptics’ eyes.

“If his daughter stays on the board, let’s just say the opportunity for further opportunities to influence the foundation would remain,” Reich said.

Folding the foundation would provide the cleanest break. But it’s no simple matter to shut down an organization that reported $439 million in assets in 2014 and spent $217 million on programs ranging from AIDS/HIV treatment overseas to helping Third World farmers.

What Bill Clinton started in 2001 after leaving the White House has mushroomed into a global force that has raised $2 billion from governments, corporations and wealthy individuals — including Trump, whose eponymous foundation donated $100,000 to it in 2009 and $10,000 the next year.

Short of locking the foundation’s doors, Hillary Clinton and her family have a few options should she win in November. To varying degrees, all the possibilities have problems:

Let someone else run it: One of the nation’s leading philanthropy experts suggests donating the whole entity to a community foundation — locally, examples include the San Francisco Foundation and the Silicon Valley Community Foundation — and have that group run it as a donor-advised fund. That means the Clintons could only advise what to do with the fund’s holdings. The ultimate authority would rest with the community foundation.

“They could give it to the community foundation to be operated in accord with the donor’s wishes,” said Leslie Lenkowsky, a professor emeritus at the Lilly Family School of Philanthropy at Indiana University and a past federal appointee of both President George W. Bush and Bill Clinton.

The advantages: The foundation could continue its charitable work, and the Clintons might be able to structure an agreement under which they could regain control of their assets after Hillary Clinton left office, Lenkowsky said.

However, such a hand-over and take-back arrangement would be “highly unusual” for a charity, said Suzanne Friday, senior counsel and vice president of legal affairs for Council on Foundations, an association of 1,300 grant-making foundations and corporations. She was speaking generally and not about the Clintons’ situation.

“There is no way to give the money back,” Friday said. “That would be contrary to the idea of an irrevocable gift.”

Break up the foundation: Clinton Foundation President Donna Shalala said last week that the organization plans to spin off many of its programs should Hillary Clinton win.

But Shalala, health and human services secretary when Bill Clinton was president, offered no estimate on how long that would take. There’s little chance it could be accomplished before a Clinton inauguration in January.

Under this scenario, the losers might be the poor and disease-ridden people who are the beneficiaries of some of the foundation’s programs. Some of the spin-offs might not be as well funded without the Clinton imprimatur.

“There is a lot of potency and cachet to the Clinton name,” said Ben Mangan, executive director of the Center for Social Sector Leadership at UC Berkeley’s Haas School of Business. “They have a convening power to bring together unlikely bedfellows that’s very unusual at that scale. To solve complicated international problems, you need proportionately large and complex answers.”

Get a new board of trustees: It’s not enough just for Bill Clinton to leave the foundation’s board, some analysts said. A whole new board, independent of ties to the Clinton family, is needed.

The Clinton Foundation’s board is packed with longtime Clinton advisers, former aides and business partners. At the center of this cozy universe is Chelsea Clinton. It’s not exactly a lineup likely to push back against the prospective first family.

“You have to change who sits on the board of trustees,” Mangan said. “If the goal is to create transparency and good governance, you can accomplish a lot of that without turning over the operation to someone else.”

To the Clintons, the disadvantage of having to answer to an independent board is that they wouldn’t have as much power in running their foundation.

Republicans, of course, are holding out for the end-it option, certain that the Clintons will never go for it and that their refusal will keep the campaign issue alive.

GOP vice presidential candidate Mike Pence has called for the foundation to be “immediately shut down.” He and Trump want an independent special prosecutor “to be appointed to determine if access to Hillary Clinton was for sale.”

The likelihood of President Obama’s Justice Department appointing a special prosecutor to investigate his fellow Democrat two months before election day is less than nil. Even an investigation might not be enough.

“Nothing will be enough for the opponents of the Clintons,” Mangan said. “Short of ending the foundation and sending Hillary Clinton to Leavenworth.”

Joe Garofoli is The San Francisco Chronicle’s senior political writer. Email: jgarofoli@sfchronicle.com Twitter: @joegarofoli