The Murdochs who run 21st Century Fox (FOXA) still have one more major hire to make at Fox News Channel, and that hiring could tell us whether CEO James Murdoch has gained any power at the expense of his father, Rupert, the company's executive chairman.

Fox News co-president Bill Shine resigned on Monday, shortly after star anchor Bill O'Reilly's dismissal following multiple allegations of sexual harassment-tied payments to women going back more than 10 years to keep such charges quiet. Shine, who has been cited in at least two sexual harassment lawsuits against Fox News, was widely viewed as a holdover who had to go.

But amid the flurry of executive changes announced on Monday, one job remained unfilled: Shine's position of co-president.

Shine shared that title with Jack Abernethy, who oversees the business side of Fox News and remains at the network. The two men, Roger Ailes loyalists, were promoted in August as a sign to O'Reilly and others that the network wouldn't drift away from its roots. Sean Hannity, another Ailes stalwart, declared last week that Fox News would be irreparably damaged if Shine were forced to resign. 

Ailes, of course, was dismissed in July after former Fox News anchor Gretchen Carlson's sexual harassment lawsuit moved other women working at the network, including star anchor Megyn Kelly, to come forward with similar accounts of boorish behavior followed by employer retaliation. Kelly left Fox News in January for Comcast's (CMCSA - Get Report) NBC News.

Technically, Fox News doesn't have a CEO following Ailes' dismissal. Rupert Murdoch held the title of acting CEO until Shine and Abernethy were promoted. Murdoch dropped the acting CEO moniker while retaining the position of the network's executive chairman. At some point, though, Shine's position will be filled, sources close to the matter said.

Who is chosen, and whether that person comes from within Fox News or from the outside, likely will indicate who's in charge: the elder Murdoch, his son James or, to a lesser extent, James' brother, Lachlan, who shares the title of Fox's executive chairman with his father.

"If Rupert is still calling the shots, they probably will go from within," said Mark Feldstein, a journalism professor at the University of Maryland and a former correspondent at ABC News and CNN. "But if James is really starting to take over, he may succeed with hiring someone from without. We're really witnessing the movement of tectonic plates generationally at Fox, and these personnel changes are being registered like little earthquakes."

Whether the Murdochs moved fast enough and with sufficient force to address longstanding complaints of sexual harassment at Fox News is open to debate. James Murdoch told investors in December that the company moved decisively following Carlson's lawsuit. Yet numerous lawsuits lodged against the company in recent weeks paint a much different picture. 

One thing is clear, and that's the Murdochs' intention to retain what Ailes built. In the wake of his departure, James Murdoch often has said that Fox News' polemic tone and conservative programming won't change.

"It would be foolish of us, if you think about the success of Fox News, both in its positioning and the voice that it has, and then where our competitors sit, whether CNN, MSNBC or others, it would be foolish of us to pursue a failed strategy instead of sticking with a winning strategy," Murdoch said in a September interview at an investor conference hosted by Bank of America (BAC - Get Report) .

In the wake of Monday's executive shuffling, Shine's programming duties have been taken over by Suzanne Scott, who worked closely with Shine. Scott was promoted to head the programming group just as Jay Wallace was promoted to head the news division.

But with numerous lawsuits still hanging above the company and reporters eager to follow the latest scandal involving the network, pressure is likely to rise on the Murdochs to hire someone who is viewed as a break with the past. That someone will be tasked with running the day-to-day operations of a business that remains the most profitable -- more than $1 billion in 2016 -- part of 21st Century Fox.

"Rupert Murdoch is probably too personally loyal to the people who came with him and would probably prefer to make as few changes as possible," Feldstein added. "The Murdochs have been so grudging, fighting these changes every step of the way, in a way that most corporations don't when they get into damage-control situations. But they really don't have a choice but to make a clean sweep."

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