May 2 (Reuters) - Proxy advisory firm Egan-Jones on Thursday recommended Norfolk Southern shareholders elect all seven of hedge fund Ancora Holdings' proposed director candidates to the railway's 13-member board and replace its chief executive officer at next week's election.

Egan-Jones is the third proxy advisory firm to support Ancora director candidates after Institutional Shareholder Services supported five of Ancora's seven nominees and Glass-Lewis backed six of the hedge fund's director candidates.

Egan-Jones said the Atlanta-based railway's board has failed its "oversight responsibilities by allowing a non-optimum approach to operational transformation" at Norfolk Southern.

Ancora has argued that Alan Shaw, CEO since 2022, should be ousted, criticizing him for failing to reach operational targets at the same time the company has faced regulatory and legal questions after a derailment last year in Ohio.

"We support Ancora's plan to replace Norfolk Southern's current CEO Alan Shaw, whom we believe has failed to exercise a creditable leadership during his tenure," Egan-Jones wrote. "A non-operational CEO has been at the helm long enough to show his inability to put the pieces in place."

Ancora has proposed Jim Barber, a former United Parcel Service executive, become CEO.

Earlier this week, ISS endorsed Shaw for election while Glass Lewis endorsed Barber for election.

Shareholders will vote to elect 13 directors at the company's annual meeting on May 9 unless the two sides reach a settlement beforehand.

"If shareholders support a majority change of the Board, they can ensure that operationally-proficient management commences a network redesign and properly implements Precision Scheduled Railroading," Ancora said.

Earlier this week, Norfolk Southern, which is valued at $52.5 billion, said replacing its board members with Ancora's candidates would "introduce significant risk, and ultimately destroy long-term shareholder value."

Many investors pay close attention to the proxy advisory firms' recommendations on how to vote on hot-button issues such as board elections and mergers, with the ISS recommendation traditionally carrying the most weight because the firm has more clients than Glass-Lewis and Egan-Jones.

Earlier in the week, investment group EdgePoint said it backed Ancora and the hedge fund has won support from unions and a large Norfolk Southern customer. (Reporting by Abhinav Parmar in Bengaluru and Svea Herbst-Bayliss in Boston; Editing by Anil D'Silva and Lincoln Feast.)