It's a warm Saturday night, and the party is getting hot at Mar-a-Lago, the Palm Beach estate that owner Donald Trump recently converted into a private club. As the Beach Boys harmonize on a makeshift stage, hundreds of revelers, many of them decked out in Hawaiian shirts, straw hats and leis, dance in the aisles and gyrate on wooden lawn chairs.

At the height of the fete, Mr. Trump asks the crowd: "Does this remind you of the Bath and Tennis Club, anybody?"

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