FORTUNE -- It's time for parts of Citigroup to be put to sleep.
That's the opinion of a group of shareholders that includes a fund managed for Benedictine nuns and a union pension plan. Recently, the two investment funds along with an asset manager Trillium Asset Management filed a proposal with Citi that calls for the bank to be broken up. The group said it asked Citi's board of directors to consider spinning off one or more of its business units. They want the board to form a special committee of independent directors to consider "strategic alternatives of the structure of the company."
Citi has struggled as of late. Last month, a boardroom drama resulted in the resignation of former CEO Vikram Pandit. Long-time Citi executive Michael Corbat took his place. The change in management has reignited speculation that the bank might decide to break itself up. Pandit had generally preferred a strategy of selling off units that got Citi into trouble in the financial crisis, like sub-prime lending, but for the most part keeping the firm intact.
MORE: Citigroup's new CEO has a lot to tackle
However, a number of former Citi leaders have recently said that it is time for the firm to be broken up. Sandy Weill, who is the former CEO and Chairman of Citigroup, and John Reed, who ran the bank before a merger with Travelers created the behemoth it is today, have both said that the U.S.'s large banks, including Citi, would be better broken up.
It appears the Benedictine Sisters of Mount St. Scholastica and the AFSCME Employees Pension Plan, which own a collective $9 million of Citi shares, are the first investors to back the break up route for Citi. The problem is the proposal lacks specifics, and at least in part seems to suffer from a lack of understanding of basic accounting.
As a reason for a break-up, Lee Sanders, chairman of the AFSCME Employees Pension Plan's Board of Trustees, cited a difference of "almost $50 billion between what Citi says its assets are worth and what the market is saying." But what Sanders is talking about is the value that Citi assigns certain assets on its balance sheet, which is based on accounting rules and not their actual value. Accounting values often don't match with reality.
"If there's not an appetite for our proposal, so be it," says Jonas Krons, who is vice president and director of shareholder advocacy of Trillium Asset Management. "But we think there should be a discussion."
What's more, it's not clear what Citi would spin off, and the proposal doesn't say. One option could be Citi's investment banking division. But selling off that unit might not generate a lot of value for shareholders. Citi's investment bank has generally been a laggard. What advantage it has comes from being tied to Citi's large bank and relatively cheap access to funds. Cut that tie, and it's not clear the unit would be worth that much. Plus there aren't a lot of buyers for global investment banks these days, since they have struggled since the financial crisis.
MORE: Jefferies flight to safety: Is this the future of Wall Street?
One business that could fetch a premium is Citi's global transaction processing unit. But that business is a consistent money maker for the bank, and didn't cause any problems in the financial crisis. What's more, it's not clear how you would separate that from the rest of its banking business. Helping people make payments around the world seems to be a core function of a bank.
Nonetheless, drum beat for break up of banks, and Citi, in particular is growing. And Corbat, inheriting a company that has consistently underperformed its peers for more than a half decade, needs to try something different. Just how a break up would happen and how successful it would be is unclear. It's messy out there.