Shari Redstone won control over her media empire in 2018 after a hard-fought struggle with CBS. In the years since, she held off on selling the family business, merging Viacom and CBS to put iconic franchises like “60 Minutes” and “Top Gun” under one roof.

Now, Ms. Redstone has decided to sell her controlling stake in Paramount, a decision that could put her in conflict with some of the company’s shareholders.

The question that Paramount’s board has to answer — and may eventually have to defend in a courtroom: Is the deal under consideration good for all shareholders, or just Ms. Redstone?

“Are these decisions that are being made in the best interest of Paramount generally?” asked Eric Talley, a law professor at Columbia. “Or are they basically the types of decisions that are only going to give Shari Redstone a nice nut but pretty much stick it to the other minority shareholders?”

The challenge lies in the company’s complicated ownership structure. Ms. Redstone’s stake in Paramount is owned by National Amusements, a holding company that she controls. She has endorsed a deal to sell National Amusements to Skydance, a media company controlled by the tech scion and Hollywood executive David Ellison. Because of the structure of the deal, the sale of National Amusements hinges on a related agreement’s being reached for Skydance to merge with Paramount.

It’s common for influential shareholders like Ms. Redstone to be paid extra for their shares, commonly called a “control premium.” Under the deal terms currently under discussion, Ms. Redstone would be paid for all of National Amusements — including its theater chain, its real estate and its controlling stake in Paramount — potentially setting up different incentives for Ms. Redstone and everyone else who owns Paramount stock.

Some Paramount shareholders have expressed concerns that any transaction based on Paramount’s currently dwindling share price might undervalue the company.

To puzzle through the options, Paramount’s board has formed an independent committee, advised by Centerview Partners and the law firm Cravath, Swaine & Moore. If the terms aren’t appealing to the board, the board can decide not to recommend it, but that would mean opposing a deal that Ms. Redstone had already signed off on.

Special committees have played a starring and consequential role in some of the most notable transactions in U.S. corporate history, like R.J Reynolds’s acquisition of Nabisco and the buyout of Dell. These directors are well aware that their actions may be scrutinized by the courts later to determine whether they worked to get the best deal possible.

“The special committee has a lot of power,” said Jim Woolery, founder of Woolery & Company, an advisory firm. “They’re risk adverse, but they want to negotiate — and be seen to negotiate — and move the thing for the Paramount stockholders.” Mr. Woolery, who has worked with many special committees, called it a “chess game.”

The committee can take steps to minimize its risk, he said, like allowing a brief period for other bidders to make another offer for Paramount. The committee could also look to secure support from a majority of Paramount’s minority shareholders and be seen as moving Skydance’s bid up as best it can.

Ms. Redstone also has options to sell National Amusements by itself, which she is prepared to pursue if Paramount’s board does not recommend a deal with Skydance. A person familiar with her priorities said she was mindful of the potential for litigation and had been careful to leave discussions about Paramount’s future to the company’s special committee. She is the chair of Paramount’s board but has recused herself from the special committee.

Skydance and Paramount recently agreed to enter into exclusive talks, a significant step toward reaching a deal. Ms. Redstone and National Amusements are encouraged by Mr. Ellison’s vision for the combined company, according to the person familiar with her priorities, who said it called for Paramount to team up with another major company on a streaming joint venture in the United States.

A deal with Skydance could bring other opportunities to Paramount, including tech and animation know-how from Mr. Ellison’s management team, which includes John Lasseter, a former Pixar executive. The plan calls for Skydance to supercharge Paramount’s streaming capabilities, improving personalization with better algorithmic recommendations and making it more efficient through better deals with data providers. Ms. Redstone is encouraged by the access to capital and tech know-how that comes with Skydance’s association with the Ellison family.

Another big selling point: Skydance has ownership stakes in Paramount’s most financially successful shows and movies, like “Mission: Impossible” and “Top Gun,” and uniting the firms would give the combined company greater flexibility in managing its franchises.

Besides Skydance, only one other suitor has emerged. Apollo Global Management, an investment firm with more than $500 billion under management, sent a letter to Paramount late last month expressing its interest in acquiring all of Paramount for $26 billion.

“It is beyond baffling to see the Paramount board of directors ignore an all-cash offer for 100 percent of Paramount,” said Rich Greenfield, a media analyst.

Paramount decided not to engage with Apollo, with one person explaining that doing so could have derailed its advancing negotiations with Skydance without certainty that Apollo’s letter would lead to a deal.

Mr. Woolery, the corporate adviser, said Paramount could use Apollo’s bid to pressure Skydance to improve its offer. He added that, in situations like these, certainty of a deal could matter more than the size of the offer. And Apollo’s bid, which was not fully financed, would have been subject to due diligence.

The Skydance deal may also be unpopular with some of Paramount’s most influential shareholders. Mario Gabelli, whose firm owns 10 percent of Paramount’s voting stock — the same class of stock the Ms. Redstone owns — said he would prefer for the company to wait at least three years before considering a deal because he believed Paramount was currently undervalued.

Mr. Gabelli also said he wanted shareholders who owned the same class of stock as Ms. Redstone to be offered the same terms she was, essentially putting everyone on equal footing.

“The voting stock, which Shari controls at National Amusements, is entitled to a premium,” Mr. Gabelli said. “The question that will be decided if she does this is whether the control premium applies to all the voting shares and not just the ones owned by National Amusements.”

Not everyone is opposed to a deal at the outset. John W. Rogers Jr., whose firm, Ariel Investments, owned 1.8 percent of the company’s shares as of the end of last year, said he was reassured by the board’s creation of a special committee and by his conversations with management and the board.

Mr. Rogers said he was open to a bid from Skydance, as he believes that both Skydance and Paramount management know that the “real value is being able to put both companies together and benefit from the synergies, the cost-cuttings.”

To get his support, it is important that any buyer “pay a price that reflects the underlying value of the all the assets,” not its current stock price, Mr. Rogers said. He said there could be additional ways buyers could create value for shareholders through a deal, like spinning off certain parts of the business, possibly to private equity firms.

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