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Shareholders will vote on whether Brian T. Moynihan can continue to be both the chairman and chief executive of the bank.Credit Simon Dawson/Bloomberg

Forget the Iowa caucuses or the New Hampshire primary. One of the more intense and dogged campaigns is currently being waged by Bank of America to convince shareholders that Brian T. Moynihan should keep his job as both chairman and chief executive.

Top bank executives and one of its board members have pounded the pavement from London to Houston, lobbying dozens of investors. They cut a deal to mollify one outspoken critic, and they enlisted the help of the former Massachusetts congressman Barney Frank, an architect of Wall Street’s regulatory overhaul. Mr. Frank said he agreed to make the case for Mr. Moynihan after discussing the issue with his neighbor, an executive at Bank of America, the nation’s second-largest bank.

The battle engulfing the bank has had, at times, the feel of a local City Council race. It has featured a cast of characters including a Roman Catholic priest, Warren E. Buffett and two giant California pension funds that have mounted an aggressive countercampaign to strip Mr. Moynihan of his chairmanship.

As many as 40 percent of shareholders were expected to vote against Mr. Moynihan from the outset, leaving about 60 percent up for grabs — a huge group that includes major money management firms like T. Rowe Price and BlackRock.

That the vote, scheduled for Tuesday in Charlotte, N.C., has proved so contentious shows the depths of discontent with Bank of America, mostly over how the bank’s board decided to give Mr. Moynihan both titles in the first place. It did so unilaterally last year, overturning a previous shareholder vote in 2009 that required the bank to have a separate chairman and chief executive.

But the battle also illustrates how the byzantine world of corporate governance can consume the time and attention of a company’s leadership.

Bank officials say Mr. Moynihan, chief executive since 2010, earned the right to also become chairman last year, having steered the company through a near-death experience after its costly acquisition of Countrywide Financial in 2008 and Merrill Lynch in 2009. They say there is no conclusive evidence that companies with separate chief executives and chairmen perform better than those that don’t divide the roles.

The two pension funds leading the charge against the bank — the California Public Employees’ Retirement System and the California State Teachers’ Retirement System — argue that an independent chairman would provide better oversight of a bank with a troubled history.

“Since Mr. Moynihan’s appointment as C.E.O. in January 2010, the company has continued to underperform, has failed important Fed stress tests, and has perpetuated a subpar engagement with its shareholders,” the California pension funds wrote in a joint letter to the bank’s lead independent director last month. “Given these missteps, we do not believe now is the time to reduce oversight of management by combining the roles of C.E.O. and chair.”

The pension funds’ sway goes beyond their less than 1 percent ownership of the bank’s shares. They have been calling and writing to the largest shareholders — including some firms they may pay to manage money on behalf of the California pensioners — urging them to vote against the combined role.

For some shareholders, the C.E.O.-chairman vote is more of an incidental bargaining chip. When the issue came up in 2009, for example, union groups that supported separating the roles were also pushing behind the scenes for the right to organize Bank of America employees, according to people briefed on the matter.

If anything, the current contest — which has reached a fever pitch this week — has been an unwelcome distraction for Bank of America just as it had put most of its legal and regulatory troubles behind it.

In 2013, JPMorgan Chase’s chief executive and chairman, Jamie Dimon, faced a similar vote, which had been stoked by the bank’s embarrassing trading loss, known as the London whale. Mr. Dimon prevailed.

Bank of America’s campaign is being run by its general counsel, Gary G. Lynch, and its head of global marketing, Anne M. Finucane, who has labored for years to burnish Mr. Moynihan’s image as a banker willing to work with regulators and community groups to right the wrongs of the financial crisis.

That image was dimmed by the board’s decision last October to overturn a bylaw that required the bank to keep its chairman and chief executive roles separate. The board argued that like most big American companies, Bank of America should have the ability to decide whether to grant its top executive one or both titles.

Still, some shareholders and others were outraged. Sensing his moment, the Rev. Seamus Finn proposed putting the issue to a vote at the bank’s annual meeting in May.

Father Finn, a Catholic priest who advises church groups on investment issues and is chairman of the Interfaith Center on Corporate Responsibility, said the leadership question was not his primary concern, but he figured that a proposal to split the role would probably get him a meeting with the bank’s top leadership.

It worked. Bank of America agreed to give Father Finn what he really wanted — a report detailing what went wrong at Bank of America during the mortgage crisis. And in return, Father Finn said he agreed to dropped his proposal to divide the top positions.

Even though the issue did not make it on the ballot at the annual meeting, the proxy advisory firms Institutional Shareholder Services and Glass Lewis urged the bank’s shareholders to vote against members of the board’s corporate governance committee because of the unilateral decision to combine the titles.

Acknowledging the extent of the shareholders’ displeasure, the bank decided to put the issue to a special vote and started campaigning.

A major player in the effort is the bank’s lead independent director, Jack O. Bovender Jr., a former health care executive and Duke University trustee. Described by a bank colleague as the consummate Southern gentleman, Mr. Bovender has been making the rounds of investors, explaining why the board moved to make Mr. Moynihan both chairman and chief executive.

Mr. Bovender has not been able to win over everyone, though. In a conversation last month, he told Institutional Shareholder Services how he agreed to take a leadership role at the bank only if no other board member wanted to step in.

Mr. Bovender was speaking “tongue in cheek,” a person briefed on the matter said. But apparently the proxy advisory firm did not see it that way, calling his anecdote “particularly telling.”

“While shareholders should be glad that Bovender stepped into this leadership vacuum by accepting the lead director role,” it wrote in its report, “it calls into question the board’s acceptance of an individual without relevant industry experience.”

With I.S.S. and Glass Lewis recommending that the jobs of chief executive and chairman be separated, the bank most likely lost as much as 30 percent of the vote because certain shareholders vote automatically with the proxy firms, people briefed on the matter said.

In trying to win over other investors, the bank has had to navigate somewhat unfamiliar territory. Each large investor approaches these votes differently. Some firms consider the opinions of their portfolio managers and analysts, who recommend whether to buy the bank’s shares. Others allow only their corporate governance committees to weigh in.

Bank of America cannot even lobby its largest shareholder, BlackRock, directly. Because BlackRock is partly owned by another bank, PNC Financial Services, the giant asset manager has to outsource its vote to an independent fiduciary so as not to run afoul of the Bank Holding Company Act.

A BlackRock spokesman declined to name the outside fiduciary, citing “company policy.”

Last week, Bank of America got a from Mr. Buffett, who said in a television interview that Mr. Moynihan deserved both titles.

Then, Mr. Frank voiced support for the combined roles, calling Mr. Moynihan “one of the more constructive” bank leaders in helping shape recent financial regulation.

Mr. Frank is not a Bank of America shareholder. But his endorsement could persuade some unions or progressive-minded investors to break from the California funds and back the bank’s position.

Mr. Frank said he volunteered to speak publicly after discussing it with his neighbor in Newton, a Boston suburb, who works for the bank in communications and public policy. Mr. Frank, who recently joined the board of Signature Bank, a small commercial bank in New York, said the most important oversight of financial companies comes not from its directors but from regulators.

“People expect too much of boards,” he said.