• Institutional Shareholder Services recommended that shareholders support five of Ancora's seven nominees and seven Norfolk Southern nominees.
• But the proxy advisory firm recommended that shareholders withhold support from incumbent board chair Amy Miles.
• ISS endorsed current CEO Alan Shaw's reelection, and while the proxy advisor said it was not supporting Ancora's CEO pick Jim Barber, it described him as a "credible" director and CEO pick.
• Glass Lewis, the other influential proxy advisory firm, recommended that shareholders support six of Ancora's seven nominees earlier this week, including CEO pick Barber.

Influential proxy advisory firm Institutional Shareholder Services recommended on Tuesday that Norfolk Southern shareholders support five of activist Ancora's seven board nominees, withholding an endorsement from CEO pick Jim Barber but describing him as a "credible director and CEO candidate nonetheless."

ISS' endorsement, included in a report viewed by CNBC, comes one day after Glass Lewis endorsed most of the activist investor's slate of nominees The endorsement also comes days after two unions came out in support of Ancora's proposed management team.

The proxy advisor recommended shareholders support CEO Alan Shaw's reelection to the board over Barber. But in a rebuke of NSC's existing governance, ISS said shareholders should not support current board chair Amy Miles.

Ancora is seeking to oust both current CEO Shaw and newly appointed Chief Operating Officer John Orr. The activist holds Shaw accountable for NSC's historic underperformance relative to peers and for a disastrous derailment in East Palestine, Ohio, just a few months into his tenure.

Glass Lewis, the other influential proxy advisory firm, said shareholders should support Barber over Shaw in its recommendation Monday. While neither endorsement suggests giving Ancora full control of the board, both provide the dissident with a clear mandate to implement change.

"The leading proxy advisory firms have collectively sent a clear message about the need for significant, shareholder-driven change at Norfolk Southern," Ancora CEO Frederick DiSanto and president Jim Chadwick said in a statement.

Investors, especially passive index-fund giants like Vanguard and BlackRock, consider proxy advisor recommendations when deciding how to vote their millions of shares. The top three shareholders at Norfolk Southern control more than 16% of shares outstanding.

ISS said in its report that it was clear "that the dissident has presented a balanced slate consisting of qualified nominees, and has generally targeted the appropriate management nominees."

"ISS's recommendation against Jim Barber is a clear indication that a change in management is not warranted," the company said in a statement, adding that his election could cause an "unfavorable" boardroom dynamic.

ISS recommends shareholders support Ancora nominees William Clyburn, Sameh Fahmy, Gilbert Lamphere, Allison Landry and John Kasich.

The proxy advisor said Norfolk Southern's governance problems were "most evident" in the board's failure to communicate with investors and prioritize their "best interests."

"As board chair, Amy Miles arguably bears the most responsibility for this state of affairs," ISS' report read.

Norfolk Southern has taken steps to address investor concerns, including appointing Orr as COO and adding two new directors, former Sen. Heidi Heitkamp and former Delta CEO Richard Anderson. ISS endorsed Anderson's election but said shareholders should not support Heitkamp.

"There is no evidence suggesting that Heitkamp is in any way unfit to serve, but dissident nominee John Kasich has comparable regulatory and administrative experience," the ISS report said, mentioning the latter's "proven ability" to foster compromise.

Norfolk Southern took issue with some of ISS' logic in its statement Tuesday, arguing that the endorsement of Ancora nominees was also a vote of confidence in Shaw's operating plan.

"The ISS recommendation relating to Ancora's nominees jeopardizes the election of Norfolk Southern's board candidates who are critical to the effective oversight of the company," Norfolk Southern said.

WATCH: CNBC's full interview with NSC CEO Shaw on activist campaign