By Liz Hoffman

Dole Food Co.’s $1.2 billion sale to its chief executive and founder squeaked past a shareholder vote on Thursday, but several large holders plan to seek a second opinion on the deal price from a judge, according to people familiar with the matter.

The buyout passed with the support of 50.9% of the shares not held by CEO David Murdock, who owns 39.5% of Dole and is trying to take it private for the second time in a decade. To pass, it needed a majority of shares not controlled by Mr. Murdock to vote yes.

But hedge funds holding at least 10 million shares — or more than 12% of Dole’s stock — have said they will seek appraisal for their shares, a legal proceeding in which a judge set a fair price, the people said. Judges in appraisal cases have often awarded more than the offer price, especially in buyouts by large shareholders like Mr. Murdock. But an appraisal can come in lower than the deal price, too, and either way resolution can take years.

The bulk of those shares are held by Merion Investment Management LP, which on Tuesday disclosed an 8.3% stake in Dole. Prior to then it hadn’t disclosed a position, meaning it owned less than 5%.

Two other hedge funds holding as many as seven million shares between them have also reserved their right to seek appraisal, according to one person. Another person put the number lower, closer to 2.5 million. A representative for Dole declined to comment, but confirmed that the company had received such notices from several shareholders.

In all, at least 10 million and possibly as many as 14 million shares have foregone the $13.50-per-share buyout offer in the hopes of getting more from a judge. Albert Fried & Co. analyst Sachin Shah said Thursday that the company could be worth more than $17 per share, including valuable land it owns in Hawaii.

This isn’t the first appraisal case for Merion, whose strategy includes buying shares of companies on the brink of a buyout and pushing for more in court.

Merion teamed with three other funds in 2011 to seek appraisal for 5.84 million shares of Cogent Inc., which had just been sold to 3M Co. This summer, a judge awarded the funds 3.5 percent more than the sale price. In 2012, the Radnor, Pa.-based fund sued for appraisal of its stake in Deltek Inc., which had been bought by private-equity firm Thoma Bravo LLC. That suit was later dismissed.

Merion is currently seeking appraisal for its 5.4 percent stake in BMC Software Inc., which it acquired weeks before the company’s shareholders voted to approve a $6.9 billion buyout by private-equity firms Bain Capital and Golden Gate Capital this summer.

Between BMC and Dole, Merion now has more than $450 million tied up in appraisals, based on the merger prices of the two deals.

Merion is run by Andrew Barroway, a former lawyer at Kessler Topaz Meltzer & Check LLP, which represents plaintiffs in big merger and securities cases. Barroway did not respond to a request for comment.

Dole’s stock price spiked briefly on news that the deal had passed and closed at $13.55.

It’s too late for investors to benefit from an appraisal, which requires shareholders to notify the company before the vote.

But a person familiar with the trading strategy said the newcomers are likely betting on a the outcome of a separate lawsuit over the deal that is moving ahead in Delaware.

In that case, shareholders accuse Mr. Murdock, who also chairs Dole’s board, of manipulating the stock price in the run up to his bid. The company canceled a planned stock buyback in May, sending shares plunging to their lowest levels in nearly a year. Dole also announced it would spend $165 million on new ships, a big upfront cost the plaintiffs say was designed to further depress the shares. Mr. Murdock announced his bid two weeks later.

And as it was telling stockholders the shares were worth $13.50, Dole was telling its banks that the company had net assets worth more than $23 per share, according to the complaint, which cites nonpublic materials shown to lenders. The company denies the allegations.

Few merger lawsuits result in more money for shareholders. Most settle, with companies agreeing to disclose more information about the deal process and to pay the plaintiffs’ attorney fees.

But the law firm for the Dole plaintiffs, Grant & Eisenhofer PA, has a string of big damages cases to its name. The firm secured multimillion-dollar payouts in litigation over the sale of Del Monte Foods Co. to KKR & Co. LP in 2011, of El Paso Corp.’s pipeline business to Kinder Morgan Corp. in 2012, and of Delphi Financial Group Inc. to Tokio Marine Holdings Inc. in 2012.

Dole’s trading after Thursday’s vote suggests investors are optimistic Dole will be the next in that line.