Activist investor Starboard Value moved Friday to dissolve News Corp’s dual-class share structure, a challenge to the Murdoch family’s control over the Wall Street Journal parent, according to people familiar with the matter.

The push was made via a non-binding shareholder resolution, said the people. News Corp’s structure as of September gave Rupert Murdoch control over around 40% of the company’s voting stock.

News Corp in a Monday statement said that the conglomerate had “thrived under the current structure,” and indicated that it would oppose Starboard’s proposal.

Starboard owns roughly 2% of the company’s Class A shares, according to FactSet data. Managing member Jeff Smith told CNBC last year the firm was pushing for News Corp to spin out its real estate assets, including an interest in REA Group of Australia.

Smith became vocal last year regarding the dual class structure: “There have been votes to declassify, it’s something to consider as well. But there are easier paths to create a lot of value.”

Murdoch is also in the midst of a legal battle to give his son Lachlan Murdoch control over the family trust which holds the News Corp stake, the New York Times and Wall Street Journal have reported.

Last November, Rupert Murdoch, 93, stepped down as chair of the board at both News Corp and Fox Corp. He is now chair emeritus of each company. His son, Lachlan Murdoch, is the sole chair of News Corp., and continued his role as Fox Corp.’s executive chair and CEO.

News Corp shares were down about 1% for the day, gaining slightly when Reuters first reported the news of Starboard’s push. Starboard has mounted campaigns at companies including Autodesk, Match Group and Salesforce.

News Corp, in addition to its ownership of the Journal, also owns The Sun and publisher HarperCollins.

Representatives for News Corp and Starboard did not immediately return requests for comment.