As a review of his Manhattan building portfolio shows, Mr. Trump repeated his Trump Tower innovation at least seven more times.

The idea quickly caught on with other New York developers looking to sell condominiums of ever loftier height, status and, most important, price. By 1985, the year after Trump Tower opened, the developer Harry B. Macklowe had employed the same stratagem to turn his 67-story Metropolitan Tower into a 78-story skyscraper.

Mr. Macklowe’s team credited Mr. Trump for the idea. So did Mr. Trump.

“A lot of people have copied me,” he told The Times in 2003.

In this case, imitation is shrewd salesmanship. One57, the billionaires’ aerie on 57th Street that laid temporary claim to being the tallest residential tower in New York when it was completed in 2014, was said to top out at the $100 million 90th-floor penthouse. Actual floor count: 75.

“The higher your building, the better it is for your marketing purposes,” said Amir Korangy, the publisher of The Real Deal, a real estate publication based in New York. “Nobody’s trying to have the shortest building in the city, so any sort of edge you can get to add a floor here and there, you take it.”

The city’s Buildings Department does not object, so long as the floors are counted accurately in the building’s certificate of occupancy.