The kitchen is about to get hotter at Darden Restaurants Inc.

Days after announcing a plan to spin off or sell its Red Lobster chain, the restaurant operator is expected to face a second activist shareholder calling for a more dramatic breakup of the company and for splitting off its vast real-estate holdings.

Starboard Value LP has taken a 5.6% stake in the company, which it plans to disclose in a federal filing Monday, according to people familiar with the matter.

The investment firm thinks the company's move to cast off Red Lobster falls short of what is needed to boost Darden's shares, the people said.

"We do not comment on specific discussions with shareholders, but in this instance, we haven't been contacted by Starboard," a spokesman for Darden said in an email Sunday.

Darden also owns the Capital Grille and LongHorn Steakhouse chains, among other brands.

In October, Barington Capital Group LP began pushing Darden to carve its Red Lobster and Olive Garden chains into a separate company, put its real-estate holdings into a separate real-estate investment trust and cut costs.

Starboard will push for a slightly different reorganization plan, according to people familiar with its intentions. Starboard wants the company's first move to be creating a REIT for its property holdings, which the firm believes would create value for shareholders. Then, it wants Darden to combine Red Lobster, Olive Garden and LongHorn Steakhouse into one company and its remaining smaller, faster-growing chains into another.

Darden has already explored options for its real estate, but last week rejected Barington's suggestions for those assets along with a broader breakup. Chairman and Chief Executive Clarence Otis said on a conference call that creating a REIT, or conducting a so-called sale-leaseback of the company's property, doesn't make sense.

Starboard, spun out of investment bank Cowen Group Inc. in March 2011, is known for launching frequent activist campaigns. This year it won a battle at Office Depot Inc. But it failed in its attempt to find a better deal for pork producer Smithfield Foods Inc. than its now-closed $4.7 billion sale to Shuanghui International Holdings Ltd.

The two activists aren't working together on Darden, though Starboard will seek talks with other shareholders and the company after reporting the stake, the people said. Activists often pile into the same stock and push for change from several angles, which can ratchet up the pressure on a company and its management. Barington has said it is in a group that holds just over 2% of Darden shares.

Starboard, which frequently seeks board seats, also believes Darden needs to improve its operations and become more efficient, the people said. They said it sees room for more dramatic costs cuts than those that have been planned by the company.

Darden has hired Goldman Sachs Group Inc. for advice amid the pressure from Barington and as it conducted a review that led to its plan to split off Red Lobster, which has underperformed expectations. The company said separating Red Lobster would help it refocus, and that keeping Olive Garden with the rest of its brands makes strategic sense.

Darden also announced plans to cut costs, slow expansion and forgo acquisitions.

Wall Street analysts applauded the plan to shed Red Lobster and cut costs, and some have come out against a broader breakup.

Darden "announced several strategic changes that we believe are a move in the right direction," Sterne Agee analysts wrote last week.

But Darden's shares dropped after the company announced its plans Thursday, closing down about 3.6% before gaining slightly Friday. It ended the week at $51.09, up 13% on the year.

Starboard took advantage of Thursday's decline to accumulate more shares and cross the 5% threshold requiring disclosure after owning the stock for several months, the people said.

Write to David Benoit at david.benoit@wsj.com

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