Passing San Francisco’s multibillion-dollar budget each year is a reliably messy process, fraught with late-night negotiations, haggling between lawmakers and pressure from lobbyists pressing their clients’ case for city cash.

But this year, with the budget process running parallel to a special election to choose a mayor, deciding the city’s finances is going to be singularly strange.

By the time San Francisco’s next $10 billion budget goes into effect Aug. 1, it could have the unprecedented distinction of crossing the desks of four different mayors in a span of eight months.

The late Mayor Ed Lee started the process, outlining goals and issuing instructions to department heads. After Lee died in December, Board of Supervisors President London Breed stepped in as acting mayor and stuck to his course.

Mayor Mark Farrell, whom the board named to the job in January after a controversial vote, has wielded the most influence over the budgeting process. On June 1, he’ll present a spending plan to the supervisors reflecting his priorities: street cleanliness, homelessness and public safety.

The board will then make changes. And at the end of July, adhering to the schedule laid out in the City Charter, San Francisco’s next mayor — having been sworn into office possibly just days earlier — will sign the budget.

Exactly what the budget will look like will also depend on the outcome of two competing measures, Propositions C and D, which would raise taxes on commercial landlords to fund child care or homelessness and housing initiatives, respectively. Millions will flow to the winning measure’s causes.

The policy and budget priorities expressed by the four leading mayoral candidates — Breed, Supervisor Jane Kim, former Supervisor and state Sen. Mark Leno and former Supervisor Angela Alioto — broadly overlap with Farrell’s. Like much of this mayor’s race, the disagreements arise mainly over details.

But all the candidates say they intend to make their own mark on the budget. To do that, the city’s mayor-elect will have to work quickly with the Board of Supervisors.

Kim said she’s confident there will be little “contradiction or tension” between Farrell’s budget and the one she would sign. “If there are differences, it’s often in the execution on how we deliver the services, rather than the funding amount given to each individual area,” she said.

Kim said she would support spending more to add to the city’s police force. She voted against a population-based police staffing plan in 2015, arguing that adding more officers doesn’t improve safety on its own. Instead, she says, the city should couple a bigger Police Department with spending on social-welfare initiatives such as after-school programs and homelessness prevention.

“I’m open to increasing the police budget (for more officers), because we hear from residents that they want to see more foot patrols and more officers addressing low-level property crime and drug dealing,” Kim said. “I just want to look at the overall budget and make sure we’re also looking at these other strategies that make us safer.”

Kim would also look to spend more on making City College of San Francisco free to city residents. Tuition is free now only in the spring and fall semesters, and Kim wants to see that expanded to the summer session.

Kim has also spearheaded Prop. C, which would raise taxes on commercial landlords to 3.5 percent to fund early childhood education and care services. It would bring in an estimated $146 million each year.

One of Breed’s top priorities is giving raises to nearly 22,000 in-home care workers, nonprofit employees and workers at San Francisco International Airport. She wants to increase their pay gradually to $16.86 an hour. Their wages will rise to $15 an hour in July, as will the pay of everyone else working for minimum wage in San Francisco. Boosting the city workers’ wages to $15.50 would cost the city about $14 million a year.

In-home care providers, Breed said, “took care of my grandmother, my aunt — they’re able to help people who can’t typically take care of themselves live in their homes with dignity.”

Breed also wants to find $4.3 million for a program to provide free legal help to people facing evictions. Proposition F on the June 5 ballot would create a similar program, but Breed favors doing it legislatively so the board can fine-tune it.

Breed would look to add funding for the city attorney’s office to handle mental health conservatorship cases. The board passed Breed’s legislation this month to shift authority over conservatorship proceedings from the district attorney to the city attorney, to ensure that such cases are handled by a civil body, not a criminal one.

Breed said she’s also “praying that Prop. D passes,” which would bring in around $70 million annually for the city to invest in homelessness and housing services. “That will be a tremendous help,” she said.

Leno has pledged to end street homelessness by 2020, and he said his budget would reflect that commitment.

A significant part of that plan involves immediately moving 1,000 homeless people into single-room-occupancy hotels. Every 50 people placed into those units would cost about $1.2 million, Leno estimates.

To Leno, homelessness represents the root of many other San Francisco problems. Taking people off the streets, he said, will cause a chain reaction of cost savings that can be directed elsewhere.

“The mess in our streets is the symptom of the problem, the problem being that we have 3,500 people living where they should never be living — on our streets,” Leno said. “There will be savings across the board by dealing with this significant and top priority.”

Leno wants to overhaul the way the city puts the budget together from the ground up. He said he would look to implement a zero-based budgeting process, in which city agencies build their spending for the coming year from scratch. The idea is to force department leaders to justify each line item in their budgets, rather than relying on a template cribbed from the previous year.

“This is how you find waste, fraud, abuse and redundancy,” Leno said. “If there are failed programs that did not bring a return on investment, you’ll catch it. We want to reinvest in programs that reached their goals and their mission, and did it within budget. It provides greater accountability.”

Alioto has made clear her disdain for the leaders of departments including the Municipal Transportation Agency and Public Works, saying they run bloated “fiefdoms” that she would reform.

Alioto said that “besides the obvious crises” such as homelessness and street filth, “what no one is talking about is our small businesses.” She says there’s too much city construction, such as MTA streetscape projects, that are hurting merchants’ ability to bring customers in the door.

“Our small businesses are going out of business,” Alioto said. “Block after block is boarded up, and it seems as though the MTA and DPW have intentionally gone after these small businesses, like taking away their parking to not allowing their customers to get to them with all the construction.”

Alioto wants more city funding for community benefit districts — merchant groups that tax themselves to provide services like sidewalk cleaning and street ambassadors — “so the communities would have more money to run their businesses.” She would also give tax breaks to small businesses by “reallocating money from other places.”

Those “other places” could be the MTA and Public Works budgets. “I honestly believe the way those fiefdoms are run is simply to the detriment of the city, and specifically small businesses,” Alioto said. “These merchants are so disgusted, and that can be stopped through the budget.”

Alioto is also a supporter of the zero-based budget system.

“It’s a clean start,” she said. “If people are relying on things that were done wrong in the past, they should know right now — don’t rely on it.”

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