Top governance experts, an activist investor and a key shareholder advisory firm are expressing concern with some Wells Fargo (WFC) - Get Report directors, suggesting that the scandal-plagued lender may have to shake up its board in the coming months.

The latest trouble for the San Francisco-based bank comes as it faces continued scrutiny after failing to prevent employees from creating as many as two million unauthorized credit card and savings accounts over a five-year period, a situation disclosed when Wells paid $185 million in a September settlement with state and federal regulators. The bogus accounts led to the dismissal of about 5,000 employees and set off a firestorm of criticism that ultimately spurred the retirement of the company's CEO, John Stumpf, and the installation of an independent board chairman.

Now, in anticipation of the bank's annual shareholder meeting on April 25, Glass Lewis, one of two major U.S. proxy advisory firms, is recommending that shareholders vote against six of the company's 15 board members. The other major proxy advisory firm, Institutional Shareholder Services, is expected to issue its report on the meeting shortly.

Glass Lewis recommends shareholders vote against four directors -- John Baker, Lloyd Dean, Enrique Hernandez and Cynthia Milligan -- on the grounds that they failed to fulfill their duties to a corporate responsibility subcommittee, according to a copy of the report obtained by TheStreet.

The committee is responsible for overseeing Wells Fargo's reputational risk, customer service record and complaints. Glass Lewis, whose recommendations carry a lot of weight with institutional investors, said shareholders should vote against the nominees "based on the reputational damage" inflicted on the company.

The proxy advisory firm also urged shareholders to vote against Wells Fargo directors John Chen and Susan Swenson, arguing that they both serve on too many boards. According to relationship mapping service BoardEx, a service of TheStreet, Chen is the chairman and CEO of Blackberry Ltd. (BBRY)  and a director at Walt Disney Co. (DIS) - Get Report  in addition to his Wells Fargo directorship. He is also a technical advisory board member at WI Harper Group Inc.

Swenson, meanwhile, is the CEO of Novatel Wireless, which is owned by Inseego (INSG) - Get Report , and a director at Harmonic Inc. (HLIT) - Get Report  in addition to her Wells Fargo work.

Ultimately, no CEO should serve on more than one additional board, said Charles Elson, chief of the University of Delaware's Center for Corporate Governance.

"How can you devote enough time to the other boards, given Wells Fargo's problems? You're a jack of all trades, master of none," Elson said. "The CEO's job is 24-7 and a board seat today, particularly at a company in trouble, represents hundreds of hours of work. The concern here is that shareholders of Wells Fargo aren't getting the board they deserve."

Glass Lewis suggested that "the time commitment required by this number of board memberships, in conjunction with executive duties, may preclude the nominees from dedicating the time necessary to fulfill the responsibilities required of directors."

The adviser's recommendations could spur an activist public pension fund to launch a so-called "just vote no" campaign against Wells Fargo directors, and it's likely to drive at least a large minority of shares to vote against the six incumbent directors.

The vote isn't binding and Wells Fargo is not obligated to remove the directors even if a majority of shares oppose the board members. However, a large negative vote could be embarrassing enough to drive the company to make changes on its own.

Wells Fargo has already come under attack by a few activist investors in the wake of the scandal, including gadfly John Chevedden, who frequently submits shareholder proposals at U.S. corporations. Chevedden sent a letter to Target (TGT) - Get Report in September urging it to remove Stumpf from its board, and he resigned from the body in October.

"They will get less votes for sure because of the recommendation," Chevedden said. "They could get 70% approval. That could get the company to make changes to the board. When a director doesn't get 92% or 95% support, he's doing something wrong."

In addition, CtW Investment Fund, an organization that advises pensions for unions belonging to the Change to Win labor group, launched a campaign in October urging the embattled bank to add two directors to its board who understand human capital management. The fund, which advises funds representing roughly 12 million Wells Fargo shares, has since placed the campaign on hold as it works directly with the bank. The Glass Lewis report could help propel that effort. 

In response to a request for comment, Wells Fargo said in a statement that its board and management team are "taking decisive actions to rebuild trust with customers, team members, community partners and shareholders."

Glass Lewis's recommendations come before a report on an independent investigation commissioned by Wells Fargo's board, which the company has promised to disclose before the annual meeting.

EXCLUSIVE LOOK INSIDE: Wells Fargo is a holding in Jim Cramer's Action Alerts PLUS charitable trust portfolio. Want to be alerted before Cramer and the AAP team buy or sell the stock? Learn more now.