Bill Gates, whose investment firm Cascade Investment Inc. is a co-owner of the luxury-hotel operator Four Seasons, is raising his stake in one of the bigger owners of high-end lodging properties.

Cascade disclosed in a regulatory filing on Monday it had acquired 1.7 million shares of Strategic Hotels & Resorts Inc. for $21.5 million in recent months. That brings Cascade's stake in the hotel real-estate investment trust to 9.8%, the filing said. Cascade owned 9.2% of the REIT at the end of 2014.

Strategic Hotels owns many luxury hotels, including the Essex House overlooking Manhattan's Central Park and the Hotel del Coronado in San Diego. The company recently began a review of strategic alternatives, including a possible sale of the company, said people familiar with the matter.

"Cascade is a major shareholder and we are open and available to talk to them," said Raymond Gellein, Strategic's chief executive officer.

Shares of Strategic were up 3.1% to 13.63 in Monday trading.

Write to Craig Karmin at craig.karmin@wsj.com

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