State treasurers from Illinois, Rhode Island and Pennsylvania, and New York City Comptroller Scott Stringer, co-filed the proposal. They oversee money including pension funds and joined activist and original filer Trillium Asset Management.
A similar shareholder proposal seeking an independent chair was defeated in 2017 at Facebook, where Zuckerberg's majority control makes outsider resolutions effectively symbolic.
Rhode Island State Treasurer Seth Magaziner said that the latest proposal was still worth filing as a way of drawing attention to Facebook's problems and how to solve them.
"This will allow us to force a conversation at the annual meeting, and from now until then in the court of public opinion," Magaziner said in a telephone interview.
A Facebook spokeswoman declined to comment.
At least three of the four public funds supported the 2017 resolution as well. The current proposal, meant for Facebook's annual shareholder meeting in May 2019, asks the board to create an independent board chair to improve oversight, a common practice at other companies.
It cites controversies that have hurt the reputation of the world's largest social media network, including the unauthorized sharing of user information, the proliferation of fake news, and foreign meddling in U.S. elections.
Illinois State Treasurer Michael Frerichs said in an interview that, while an independent chair might not have prevented all the issues, "there might have been fewer of these problems and less of a drop in share price" at the company.