Never mind that last year he bought a small condo at Trump Parc, two months after buying a neighboring 110 Central Park South apartment for $4.31 million.

But none are for him. Reached through his lawyer, the 76-year-old, who speaks in the beatific and regal accent of a Gabriel García Márquez villain, turned out to be a massive Manhattan landlord. “I tell you, I started buying apartments in New York maybe 30 years ago, 25 years ago,” Mr. Azcárraga Madero said. “At that time no one wanted to live in New York, and the prices were ridiculously low.”

When he and his wife, Lorenza, come to the city about every two months, they stay in their four-bedroom apartment at Trump Parc; everything else they rent out. “We own over 65 apartments,” he said—though city records don’t show quite that many for his holding company, Central Park Realty.

The couple won’t be staying at their newly refurbished Plaza unit, but they’re not alone: An Italian yachtsman, two Miami doctors and a natural-sweeteners executive (all with cheaper Plaza apartments) were described as recent buyers with “second thoughts” in a Sunday New York Times article.

Mr. Azcárraga Madero—the son of a RCA Victor salesman, he said, and now the owner of 108 radio stations—has had offers of “around $40,000 a month” for the apartment, whose two bedrooms overlook Central Park.

And the $5.3 million penthouse duplex at 715 Park, shown here, that he bought the same week? “That’s a beautiful penthouse with terraces—Elizabeth Taylor lived in that Park Avenue apartment for many years,” he said. On the flip side, he sold a Sherry-Netherland co-op across the street from the Plaza for $3.65 million in August.

In Mexico, do people complain that he owns too much? “No, no, because there are over 1,500 radio stations in Mexico,” he said, “and it’s pretty well divided.”