More than a decade since San Diego switched to a new form of government with the mayor as City Hall’s chief executive, we’re still learning how it works.

Monday, members of the City Council found out that to change the city budget the mayor proposes each year, they ultimately need a supermajority of six votes, not just a simple majority.

The mayor announced plans late Monday to not only veto part of the City Council’s budget but also add to it funding he wants to fund a contentious special election so San Diegans can vote later this year – instead of during the 2018 general election – on a proposal to expand the convention center, and a plan to redevelop the Qualcomm Stadium site.

Vetoes of budget items have happened twice since the switch to a strong mayor system — former Mayor Bob Filner and former Mayor Jerry Sanders both issued veto statements. Both of those, however, simply rejected spending proposals. Neither wanted to add money elsewhere, unilaterally.

Mayor Kevin Faulconer must take several steps to get what he wants – including modifying a line item to add money and then making cuts in perhaps several other areas.

Faulconer’s power move reveals how little control over the budget the City Council actually has. Yes, a Council majority can set the city’s budget, but the mayor has wide authority to disregard and modify those changes.

The revelation that the mayor can not only veto spending plans but modify others as he wishes came during the climax of Monday’s tense City Council meeting.

City Councilman Mark Kersey had earlier hinted that the mayor may veto the Council’s decision not to set aside money for a special election in November.

This was the mayor’s proposed budget for that.

The City Council was about to cut that line item for elections from $6.5 million to $1.5 million. The mayor estimates the special election will cost $5 million.

But then Councilman David Alvarez asked for clarification from City Attorney Mara Elliott.

“I’d like the city attorney’s office to clarify that the mayor’s veto authority is only to eliminate what is being funded in this budget not to add anything that’s not in this budget, is that correct?” Alvarez said.

Elliott then pulled up the City Charter and began reading from it. “Could you just give us about one minute here?” she said.

Finally, her deputy whispered to her.

“So Deputy City Attorney Brant Will just said the mayor can change whatever he wants. That’s the easiest summation of Charter Section 69,” she said.

The mayor can change whatever he wants, and he plans to.

He has five days once the budget has been sent to him to return his changes. And they could be rough for the City Council. The mayor could cut district priorities some of them are concerned about, and they would have no recourse unless they can find a sixth vote to override him. The Council is made up of five Democrats and four Republicans.

“If the City Council makes radical changes to the budget with effects on San Diego’s future, they should expect to need a supermajority to do that,” said Matt Awbrey, the mayor’s director of communication.

Alvarez said he needed more detail on this newly discovered aspect of city budgeting.

“I look forward to the city attorney’s clarification of the mayor’s powers under Charter Section 69,” he said in a statement. “I do not believe the mayor ‘can do whatever he wants.’”

Councilman Chris Cate voted for the budget but supports modifying it to include money for the special election. He said this issue hasn’t come up in the past because there has not been a budget issue quite this controversial since the strong-mayor form of government was put in place in 2006.

“I think the mayor is in a position to exert his authority, and the Council is going to have to deal with it,” Cate said.

I asked Cate what the mayor would cut to make room for the $5 million he wants to add back in to the budget.

“That is a good question,” Cate said. He mentioned money that was set aside to help pay down the debt remaining on Qualcomm Stadium as a possible place to find money.

The city attorney’s statement that the mayor could change whatever he wanted in the budget surprised many watching the meeting. City staff circulated the language in the City Charter giving him power over the budge to “either approve, veto, or modify any line item approved by the Council.”

“That’ll be a fun city attorney opinion to read,” wrote Gil Cabrera, chairman of the Convention Center Corp. and a lawyer who ran against Elliott for city attorney.

“What is the point of [City Council] review and vote if ‘the mayor can do whatever he wants?’” asked Carol Kim, political director of the San Diego Building Trades Council.

The city attorney’s office would not comment on the issue. Spokesman Gerry Braun said the office was preparing a memo to answer questions from the City Council.