Who will succeed Disney CEO Robert Iger in 2016?

It’s one of Hollywood’s longest-running guessing games: Who will succeed Walt Disney Co. Chairman and Chief Executive Robert Iger? And it just got a little more interesting.

Anne Sweeney’s announcement this week that she will step down as head of Disney’s media networks, including ABC-TV, could help set up important moves on a corporate chess board as Disney prepares for bigger and more dramatic changes.

Iger agreed last summer to stay on as CEO through June 2016, 15 months longer than initially planned. That has extended the day of reckoning for choosing his successor, who many think will be either Chief Financial Officer Jay Rasulo or Thomas Staggs, who runs the theme park division.

Sweeney was not considered a top contender, but her departure could now give Iger an opportunity to test another executive in the TV division, where Iger himself earned his stripes. At a company like Disney, with 175,000 employees and $45 billion in yearly revenue, the board would typically consider outside candidates as well — as it did in 1984 when it hired Michael Eisner.

PHOTOS: Upcoming Disney fall films and beyond

“What you have to do in a situation like this is think the unthinkable,” said veteran executive recruiter Stephen Unger, who has conducted a search for a Disney board member on behalf of the company. “Every option is on the table.”

One name that has surfaced recently is Sheryl Sandberg, the powerhouse Facebook executive who joined the Disney board in 2010. Considered a rock star among professional women, Sandberg is probably best known for her 2013 bestseller, “Lean In: Women, Work, and the Will to Lead.”

Sandberg, 44, has the kind of resume that might be useful at Disney, especially as social media and the Internet become increasingly important as entertainment portals. Before joining Facebook as chief operating officer, the Harvard graduate was a top executive at Google. She also has Washington experience — serving as chief of staff to former Treasury Secretary Lawrence H. Summers — a valuable asset for a company with a big media portfolio.

People close to Sandberg dismiss media reports that she is a contender, although neither Facebook nor Sandberg is responding publicly to the speculation.

Whoever gets the job, Iger will be a tough act to follow. Since he took the reins of the Burbank entertainment giant in October 2005, the value of Disney’s stock has more than tripled. Iger orchestrated Disney’s multibillion-dollar acquisitions of Pixar Animation Studios in 2006, Marvel Entertainment in 2009 and Lucasfilm (with its “Star Wars” franchise) in 2012 — three deals that transformed the company and established robust content pipelines for years to come.

PHOTOS: Disney’s animated lineup from 1984-1994

What’s more, Disney’s core animation film division is riding high once again, with last year’s “Frozen” on track to become the biggest-grossing animated film in history. The film has taken in more than $1 billion and is still playing in theaters four months after its release.

And there’s more to come. Two of Iger’s highest-profile projects are scheduled to debut six months before his planned departure. The Shanghai Disney Resort, a nearly $4-billion theme park project that Iger has been working on for more than 15 years, is slated to open by Dec. 31, 2015. That same month, the first Star Wars film in a decade is expected to hit theaters.

The contract extension ensured that Iger, 63, would be the CEO during those highly anticipated milestones.

Disney first announced in 2011 that Iger’s tenure would end in 2015, keeping with Disney’s penchant for long-range planning.

But more time isn’t necessarily a good thing when it comes to a succession race, as evidenced by the contentious bake-off at Warner Bros. last year. In that case, three executives openly jockeyed for more than two years for the top job, triggering instability and competition. Within three months after Kevin Tsujihara took over as studio chief last March, rivals Jeff Robinov and Bruce Rosenblum left the company.

PHOTOS: Disney without Pixar

At Disney, succession is a fine art. Each year, senior executives must identify who would be the best candidates to replace them should such a move become necessary.

Sweeney announced this week that she would leave the company by January. Iger plans to quickly find a successor to run ABC and related units, including ABC Family, Disney Channel and ABC radio.

If Disney were to use the TV job as a means to provide more executive seasoning, it wouldn’t be the first time.

In January 2010, executives Rasulo and Staggs swapped jobs in a move widely seen as a way to broaden the executives’ experience and see how they would perform in different roles.

Rasulo, a native of New York, joined Disney in 1986 after two years as a manager at Marriott Corp. He had a long stint as head of the parks and resorts division before taking Staggs’ place as chief financial officer. During his parks tenure, Disney opened Hong Kong Disneyland and began a massive remodel of the California Adventure theme park in Anaheim.

PHOTOS: Celebrities by The Times

Rasulo was also previously chairman and CEO of Euro Disney. He has been credited with revitalizing Disneyland Paris, which opened in 1992 to poor reviews and with a large amount of debt. Rasulo joins Iger for quarterly earnings calls with analysts, providing details of the company’s financial performance, and regularly speaks at business conferences and summits.

Staggs, an Illinois native, signed on with Disney in 1990 after serving as an investment banker for Morgan Stanley & Co.

Since Staggs joined the parks group, the division has doubled the size of its cruise line fleet and launched MyMagic+ to allow theme park visitors to more efficiently tour the attractions. The MyMagic+ bracelet given to guests also doubles as a hotel room key and theme park ticket and can be used to make purchases. Disney rolled out MyMagic+ at Disney World last year, and the system is expected to be introduced at other properties.

On Wall Street, at least, investors consider it a two-way race between Staggs and Rasulo, according to Laura Martin, a senior analyst at Needham & Co.

With the notable exception of Eisner, Disney usually selects its chief executive from within. The hiring of super-agent Michael Ovitz as president in 1995 led to one of the stormiest chapters in the company’s history.

FACES TO WATCH 2014: Digital media

“It is a tight and difficult culture, one that would be very difficult for outsiders to break into,” Jeffrey Cole, director of the Center for the Digital Future at USC Annenberg School, said. “You’d have to be twice as good to come in from the outside.”

At the same time, Iger’s decision to hire Alan Horn as studio chief after a long stint at rival Warner Bros. is considered a success. Despite Disney’s strong bench, an outside hire shouldn’t be discounted, said Unger, who has led CEO searches for IMAX Entertainment, Telemundo and Public Broadcasting System.

“They’ve made a lot of the right steps in terms of developing their executives,” Unger said. “But I am quite sure if a spectacular executive appeared the Disney Co. has an obligation to its shareholders to pick the best person and not just reward somebody because they are within the company.”

Iger served as president and chief operating officer for five years before being promoted to CEO in October 2005. He earned his management stripes at ABC, where he began his career 40 years ago. Iger, who is married to TV news personality Willow Bay, was named chairman of Disney in March 2012.

He is scheduled to vacate his two positions when his current deal ends on June 30, 2016. When the board extended Iger’s contract last year, its independent lead director said it did so because of his “outstanding leadership” and for his “unique ability to drive creative and financial success” at the Burbank giant.

And Iger’s contract could be extended again.

“He is the dean, the real leader of the entire entertainment industry,” Cole said. “It’s tough to give up a job that has that much power ... and the board just adores him.”

[email protected]

[email protected]

Times staff writer Jessica Guynn contributed to this report.