The revolt in the wake of last year's $6.2bn (£4bn) London Whale trading loss has been aggravated by a decision to cut off dissident shareholders' access to voting information ahead of the bank's annual meeting on Tuesday.
Last year a proposal to split Dimon's roles as chairman and chief executive gained 40% of the vote.
But that vote came before the magnitude of the incident was clear and ahead of regulatory and internal reports that have been highly critical of the failures of oversight at the bank.
A vote to strip Dimon of the chairman's job, while not binding, would be a heavy blow and there have been reports that he has considered resigning if he does not keep both titles.
Shareholders also intend to vote against the reelection of several other directors over their role in the trading fiasco.
Last year's vote was sponsored by the American Federation of State, County and Municipal Employees (AFSCME) pension fund.
This year support for the vote has grown and AFSCME has been joined by employee retirement plans for New York city and the state of Connecticut, as well as the UK's Hermes fund managers.
The split has the backing of major investors and the influential advisory firms Institutional Shareholder Services and Glass, Lewis & Company.
But Dimon has fans too. The T Rowe Price group, one of the firm's top 10 investors, has publicly backed Dimon ahead of the meeting, an unusual move for a large shareholder.
Prof Peter Henning of Wayne State University in Detroit said he expected the roles would not be split. He said the bank's financial returns had been exemplary, though "hubris" had clearly played a part in the London losses.
"There are good reasons why the roles should be split that have nothing to do with the Whale. This shouldn't be a referendum on Dimon," he said.
"The problem is that there is no guarantee that an independent chair would give any greater degree of oversight."
But Prof Charles Elson, corporate governance expert at the University of Delaware, said it was clear the roles should be split.
"The chairman of the board is there to monitor the CEO. A good CEO recognises that," he said. "Titles have meaning."
Last week the split's backers were denied access to a running tally of how the vote was going.
Broadridge, the firm that collated the votes, was asked to restrict access by the Securities Industry and Financial Markets Association, Wall Street's main lobby group. As the banks are its clients, Broadridge said it was contractually obliged to comply.
The split's supporters argue JP Morgan has been handed an unfair advantage in the final stages of the fight. Large index funds, for example, often wait until the last 48 hours to cast their vote.
The Council of Institutional Investors, whose members manage $3tn of assets in total, is now lobbying for the Securities and Exchange Commission to review the situation.
Shares of JP Morgan Chase have been broadly flat since December 2006, when Dimon assumed the chairmanship.
But the bank has significantly outperformed its peers and Dimon is credited with steering the bank through the credit crisis with aplomb.
Dimon initially dismissed the Whale losses as a "tempest in a teapot" but the losses rattled Washington and led Barack Obama to push for tighter regulation of Wall Street. Dimon's thinking on the situation seems to have evolved too.
In April he told shareholders the loss was the "stupidest and most embarrassing situation I have ever been part of".
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