By Heather Haddon and Suzanne Vranica

McDonald's Corp.'s board is coming under scrutiny from some investors and corporate-governance groups for failing to fully uncover the extent of former Chief Executive Officer Steve Easterbrook's inappropriate relationships with employees when concerns first emerged last year.

The fast-food giant Monday sued Mr. Easterbrook, accusing the CEO of lying to investigators to cover up relationships with employees to protect his multimillion-dollar severance package. The suit, a rare airing of corporate dirty laundry, follows the board's decision to fire Mr. Easterbrook without cause last November after he acknowledged a consensual sexting relationship with an employee.

Outside counsel conducted an investigation into Mr. Easterbrook last fall and shared results with the board, which accepted Mr. Easterbrook's word that it was his only relationship with a McDonald's employee, according to the complaint. Because the board fired the CEO without cause, he was able to walk away from the company with a severance package valued at tens of millions of dollars.

McDonald's now says that Mr. Easterbrook allegedly engaged in sexual relationships with three additional employees in the year before his firing, relationships that it says came to light in a wider review of Mr. Easterbrook's texts and emails after McDonald's received an anonymous tip in July. The company now says he should have been fired for cause, and it is suing to reclaim his severance, now estimated to be worth $57.3 million, according to the executive-pay firm Equilar.

Representatives for Mr. Easterbrook couldn't be reached for comment.

Some investors and corporate-governance groups say the board must now defend its initial investigation and stewardship of the company to shareholders.

New York City Comptroller Scott Stringer, custodian of the city's pension system, said that while he is encouraged that McDonald's is seeking to claw back Mr. Easterbrook's severance, the company's investigation appears to have been flawed.

"McDonald's must go further by overhauling its sexual-harassment prevention policies and setting a strong tone at the top," he said in a statement Tuesday.

Chris Kempczinski, who succeeded Mr. Easterbrook as CEO in November, pledged to overhaul the company's culture after assuming the job and outlined his plans to renew company values late last month.

CtW Investment Group, a union-affiliated fund that advanced an unsuccessful shareholder proposal to block Mr. Easterbrook's severance package at McDonald's annual meeting in May, said the company's suit shows the board's investigation was insufficient. CtW had urged investors to vote against long-tenured board chairman Rick Hernandez and compensation committee head Richard Lenny earlier this year. This week it called for their resignations.

"McDonald's current board of directors is simply not up to the task of overseeing the company for the long term," said Dieter Waizenegger, CtW's executive director.

Mr. Hernandez said that the board immediately investigated both complaints against Mr. Easterbrook with outside counsel. The second investigation made clear that Mr. Easterbrook had lied and destroyed evidence regarding the extent of his behavior, and when that came to light, the board unanimously moved to take legal action, he said.

"His misconduct, which clearly deviated from McDonald's values, must not be ignored," Mr. Hernandez said in a statement to The Wall Street Journal.

McDonald's board includes Ancestry.com LLC Chief Executive Margaret Georgiadis, Target Corp. Chief Operating Officer John Mulligan, Abbott Laboratories Executive Chairman Miles White and Paul Walsh, chairman of Compass Group PLC.

Those board members couldn't be reached for comment.

After learning of the July complaint from an employee, the board immediately called for a new investigation, according to a person familiar with the matter. The board also advised management to further highlight ways for employees to report company concerns.

McDonald's sales and profit rose during Mr. Easterbrook's four years as CEO. He cut costs, pushed to update restaurants and added new menu items including fresh-beef patties and all-day breakfast.

Under Mr. Easterbrook's watch, a party culture flourished among some senior managers at the company, former employees and others connected to the company said. Those people said the former CEO frequently socialized at Chicago bars and sporting events with employees, and flirted with some female employees. Rumors about Mr. Easterbrook's alleged conduct had reached some other company leaders in the year leading up to the first investigation, one person said.

The allegation of further relationships "calls into question the vibrancy of the first investigation," said Charles Elson, a corporate-governance professor at the University of Delaware.

Outside counsel working for McDonald's last fall reviewed backup data for Mr. Easterbrook's company-issued phone and iPad but found no evidence of improper relationships with other employees, according to the complaint and a person familiar with the investigation. Investigators looked thoroughly through those devices, but records of dozens of nude photos discovered later had been destroyed on that equipment, the person said.

Mr. Elson said directors serving on multiple boards can be distracted from an internal investigation into an executive. Seven out of McDonald's 11 nonexecutive members serve on other boards; average tenure for board members is about nine years, with its longest-serving member, Mr. Hernandez, at 24 years.

Mr. Hernandez said in a letter to shareholders earlier this year that the company was committed to bringing new members to the board, and that half of its directors had joined in the last five years.

In the wake of the #MeToo movement, companies created policies and procedures including compliance hot lines and "warm lines" for employees to raise concerns about situations inside their companies, though some human-resources professionals say meaningful change remains a ways off.

Laurie Ruettimann, a human-resources consultant who works with Fortune 500 companies, said the board should have conducted a more-thorough investigation in response to Mr. Easterbrook's breaking of company rules on relationships with employees. The fast-food giant has a longstanding policy against employees' having relationships with direct and indirect reports at all levels, which the company has said extends to the CEO.

Given how much companies can find out about their employees nowadays, it is surprising the initial investigation failed to discover the other alleged relationships, she said.

McDonald's has long maintained hot lines for employees to report complaints. The employee who made the complaint in July did so after a town hall meeting in which executives encouraged workers to come forward with concerns, the person familiar with the matter said. McDonald's sent out a company message Monday telling employees that they wouldn't face retaliation for reporting any perceived misdeeds.

McDonald's had told investors ahead of its annual meeting in May that the board's decision to negotiate a settlement with Mr. Easterbrook and fire him without cause was the best route to an orderly transition, according to a report by proxy-advisory firm Institutional Shareholder Services.

ISS also met with CtW, the union-affiliated fund, before making a recommendation to shareholders in May. ISS recommended that shareholders vote against CtW's proposal because it said there wasn't sufficient evidence that the board had acted in poor judgment. Shareholders approved the pay package and the board nominations.

"The company really lobbied investors hard that they had gotten to the bottom of this and fixed it up," said Patrick McGurn, ISS special counsel.

McDonald's now will have to make a stronger case that its board members were right to offer the initial severance, Mr. McGurn said.

"People were willing to give the board the benefit of the doubt, but there may be repercussions going forward," he said.

Write to Heather Haddon at heather.haddon@wsj.com and Suzanne Vranica at suzanne.vranica@wsj.com