Shanghai Fosun Pharmaceutical Group Co. and its partners agreed to acquire hospital operator Chindex International Inc. for about $433 million, after raising their offer to counter another bidder.

The group comprising Fosun Pharma, TPG Capital and Roberta Lipson, Chindex’s chief executive officer, boosted its offer for the hospital operator to $24 a share from $19.50, the Chinese drugmaker said yesterday. Chindex, based in Bethesda, Maryland, signed an amended agreement with the group after another bidder, who earlier offered $23 a share, declined to bid further, Chindex said in a separate statement.

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