San Francisco Mayor London Breed is planning to roll out an unusual and elaborate proposal in an attempt to unlock some of the money brought in by Proposition C, the November ballot measure that raised taxes on big businesses to fund homelessness programs.

Breed is expected to introduce legislation Tuesday that would give individual businesses subject to Prop. C’s tax the option of letting the city keep the money they pay — even if the courts ultimately strike down the measure and order the funds repaid.

While Prop. C passed with more than 61 percent of the vote, the hundreds of millions of dollars it’s projected to bring in annually will be collected — but not spent — until a legal dispute over the measure’s margin of victory is resolved.

The process could take years, stymieing the city’s ability to spend any of the money in the meantime. And if the courts deem the measure unconstitutional, the city would be forced to refund Prop. C revenue back to businesses.

But under Breed’s proposal, which she’ll co-sponsor with Supervisor Vallie Brown, a company could choose to let the city keep some or all of the money it paid under Prop. C if the city loses its court case. In return, the company would get a 10 percent tax credit on the money it lets the city hold on to, and the city would be able to spend the money immediately because the possibility of having to refund it would be eliminated.

Whether the 10 percent credit would create enough incentive for major corporations to abandon money they could potentially win back remains an open question. But perhaps the measure’s most prominent backer was a business titan — Salesforce CEO Marc Benioff — who donated substantially in the run-up to the election, framing it as a moral imperative for confronting homelessness in San Francisco.

“This is an opportunity to free up funding for homelessness now so we can put it to work helping people who are suffering on our streets,” Breed said in a statement Friday. “We know this funding could be tied up in litigation for years, and while we wait for the legal issues to be resolved, with this legislation we can start building shelter beds, mental health beds and affordable housing now.”

Representatives for Breed have spent at least the past week quietly lobbying businesses to consider signing the waiver, according to three people with knowledge of the situation who spoke on condition of anonymity. It’s not clear if any business has yet agreed to waive its right to a refund if the measure is deemed unconstitutional.

Prop. C levies an average of about 0.5 percent in gross receipts tax on corporate revenue above $50 million. There are between 300 and 400 companies in San Francisco subject to the tax, which would bring in up to $300 million annually to pay for housing, shelters, mental health treatment and other services. The Hearst Corp., owner of The Chronicle, is subject to the tax.

The treasurer’s office expects the first payments to begin arriving in April. But in order to spend any of that money, City Attorney Dennis Herrera’s office will have to convince the courts that Prop. C — as well as two other 2018 ballot measures — was passed legally.

For more than two decades in California, since voters approved Proposition 218, passing a new tax measure where the proceeds are used for specific purposes has required a two-thirds majority. But last year, a memo from the city attorney’s office interpreting a recent state Supreme Court ruling argued that proposed tax measures put on the ballot by citizens — and not government officials — required only a simple majority to pass.

Three tax measures passed with simple majorities last year but up to $500 million a year in funding for homelessness, child care and teacher salaries now depends on whether the courts agree with Herrera’s reading of the state Supreme Court’s intentions. Herrera is now confronting multiple court cases in which he’ll attempt to prove the simple-majority threshold was appropriate.

Breed opposed Prop. C prior to the election. Though she thought the measure was well-intentioned, she said it lacked accountability provisions to ensure the money was spent as it was intended.

After the measure passed by a wide margin, she said she would use her office to honor the will of the voters. Shortly after the election, Breed authorized Herrera to take proactive steps in court that would begin the process of validating the measure.

Dominic Fracassa is a San Francisco Chronicle staff writer. Email: dfracassa@sfchronicle.com Twitter: @dominicfracassa