One of the biggest pension funds in the US is going after Bank of America CEO Brian Moynihan

One of the biggest pension funds in the world is going on the offensive against Brian Moynihan and Bank of America, and reaching far back into its playbook to do so.

The California State Teachers' Retirement System (CalSTRS) earlier this month sent a letter to Bank of America detailing its opposition to the plan to install CEO Brian Moynihan as chairman.

It also sent the Securities and Exchange Commission a copy of the letter - a move that allows CalSTRS to take its argument to other shareholders and try and sway opinion against the leadership consolidation plan. That's something it hasn't done in at least two years.

"We are planning to speak with as many shareholders as will take our calls," said Mastagni CalSTRS portfolio manager Aeisha Mastagni told Business Insider on Monday. "Since [Moynihan's] appointment it has severely underperformed all its major competitors."

Mastagni declined to identify the shareholders with which the pension fund has spoken.

CalSTRS is the second largest public pension fund in the US, and one of the biggest in the world. It had assets totaling around $191.3 billion as of July 31, 2015.

As shareholder opposition grows to Bank of America's plan to let Moynihan simultaneously occupy chairman and CEO roles, more voices on both sides of the argument have sought to be heard.

Already, shareholder advisory services including Glass Lewis have told clients it does not support Bank of America's decision. CalSTRS emerged two weeks ago as one of the opponents of Moynihan's leadership consolidation plan, joined by pension CalPERS and CtW, an investment fund operating on the behalf of other pension clients.

Christina Rexrode and Joann S. Lublin at The Wall Street Journal reported Monday that Trillium Asset Management has voted against the proposal, and that Korea Investment Corp., South Korea's sovereign-wealth fund, also plans to vote against it.

Some bank officials have been telling investors the vote could go either way, according to the report.

Moynihan has his supporters too. They include Warren Buffett. Buffett, who is a non-voting stakeholder in Bank of America through a preferred stock and warrants deal, said on Sept. 2 through a spokeswoman that he is "100% in support of Mr. Moynihan."

We reached out to Bank of America for a comment and will update this article when they respond.

The bank has previously said that it views the push to consolidate its leadership as a step toward aligning itself with marketplace standards, and not as a deviation from sensible governance.

"The board believes that having the same flexibility on board leadership that 97 percent of the S&P 500 now have, while still providing strong independent oversight, is in the best interest of stockholders," a spokesman for the bank told Business Insider earlier this month.