Following the rejection of New York City Comptroller Scott Stringer's request to remove Mark Zuckerberg from Facebook leadership, another shareholder vote is already in the works to enthrone an independent chairman to lead the company.

Multiple outlets confirmed on Tuesday that Stringer, who has control of around $785 million Facebook shares, proposed during last week's annual shareholder meeting to oust Zuckerberg. According to Business Insider, 68 percent of outside investors voted for the proposal.

As part of the investors' meeting, a demand to abolish the social media giant's dual-class structure was also proposed. Unsurprisingly for many industry experts, 83.2 percent of shareholders voted for the proposal.

Stringer decided to publicize the results of the shareholders' meeting after Facebook management rejected both proposals. The investor then wrote a letter to the company's chief independent board member Susan Desmond-Hellmann.

For Stringer, Zuckerberg has "outsized" power over the company. He noted that the company chairman is "accountable to no one" and this could lead to oversights in operations. "Facebook's insular boardroom must be cracked open because the company has no accountability to its users, its investors, or our democracy," Stringer told the outlet.

Stringer said he is hoping for improved results during the second shareholder's vote that could potentially see Facebook being led by an independent chairman who will lead the social media network towards change.

Over the last few months, Facebook has been under watchful eyes following the Cambridge Analytica breach that unraveled potential security and information leaks in the social media platform's security system.

While Zuckerberg brushed off the latest move to remove him from the chairmanship, some industry analysts noted that the internal contradiction between the management and shareholders could play a key role in Facebook stocks this year.

According to BBC News, among the investors who believe Zuckerberg should step down as the chairman of the board is Trillium Asset Management. For this particular shareholder who controls around $7 million of the company's total shares, Zuckerberg can focus on being the CEO if he entrusts the board chair seat to someone else.

Facebook has been embroiled in multiple scandals over the last few months including rage over election campaign manipulation by some groups. User privacy and data protection are also still the primary reasons for concern among both users and analysts.

Industry experts noted that Zuckerberg could have lost to the votes if he didn't control around 60 percent of the board's voting power and if he voted against himself. This scenario is unlikely at this point, even if the U.S. Justice Department could look into Facebook business practices for potential antitrust violations.