NEW YORK (Reuters) - Two more U.S. proxy advisory firms on Tuesday urged News Corp investors to support a hedge fund's campaign to change the company's dual-class share structure, saying no investor should have voting rights that are different from others.

Egan-Jones and its bigger rival Glass Lewis recommended investors back a recapitalization plan at the company's Nov. 20 meeting where all stock would have one vote for one share. They join prominent proxy advisory firm Institutional Shareholder Services, which last week urged News Corp investors to do the same.

Voting for the nonbinding shareholder proposal, which was made by hedge fund Starboard Value, would be a signal that investors are intent on breaking Rupert Murdoch's control over the media empire that publishes the Wall Street Journal.

Hedge fund Irenic Capital Management, which has also been pushing News Corp for changes, on Tuesday said it will back Starboard and vote to eliminate the dual-class structure.  

"The economic stake of each shareholder should match their voting power and ... no small group of shareholders, family or otherwise, should have voting rights different from those of other shareholders," Glass Lewis wrote in its report, which was seen by Reuters. 

In its report, seen by Reuters, Egan-Jones wrote: "A one vote per share principle would provide an equitable approach to ensure that shareholders are given a fair voice that is proportionate to their stake in the Company and would be able to hold the management accountable of their actions through casting a vote."

The two recommendations, issued on Tuesday, come just days after the largest U.S. proxy advisory firm, Institutional Shareholder Services, threw its weight behind Starboard Value. Starboard, the activist investment firm run by Jeffrey Smith, submitted a nonbinding proposal to eliminate dual-class share structure, Reuters reported in September.

Murdoch and his family own a 14% economic stake in the company but control 41% of the votes. 

News Corp has urged investors to vote against Starboard's proposal. The company has argued the dual-class capital structure provides key protections for editorial integrity.

Australian governance advisory firm Ownership Matters also recommended that investors vote for the Starboard proposal. Roughly 15% of the voting shares are held in Australia and Ownership Matters is a key proxy advisory firm in the country.

Glass Lewis noted that Starboard, and other hedge funds, have also criticized News Corp for its financial performance and wrote that if the dual-class structure were eliminated, the board could potentially face a proxy fight that would likely focus "squarely on the historical performance of News Corp." 

The company could take actions to address investors' valuation concerns but keep its dual-class structure even in the face of governance best practices, the report said.

Irenic, which is run by Adam Katz and Andy Dodge, also said that its vote to end the two-class structure does not signal unhappiness with the News Corp management. Rather, Irenic said it believes "management is working earnestly to take concrete actions to unlock immediate value."

It also said it wants News Corp to pay a substantial premium to Class B shareholders, who currently have greater voting power, to convert to a structure where all shares have equal voting rights.