Demolition of Tiffany’s 1980 rooftop addition is underway on the southeast corner of 57th Street and Fifth Avenue.  A Louis Vuitton store is in the foreground, at left

The Tiffany flagship received a rooftop addition of masonry and glass in 1980.  It was used for office space and storage.

The current Tiffany flagship at 727 Fifth Avenue around 1940, the year it opened  It was designed by the architects Cross & Cross in what the Times called a “conservative modern” style.

Tiffany’s fifth flagship store, on Fifth Avenue and 37th Street, around 1905, the year it opened.  Designed by McKim, Mead & White, it was modeled on the 16th-century Palazzo Grimani on the Grand Canal in Venice. It still stands today.

Tiffany’s fourth New York City flagship store, at 15 Union Square West, around 1890.  The cast-iron facade was stripped of projecting ornament in the 1950s, but the ghostly silhouettes of some Tiffany arches can still be seen at night behind the building’s dark-glass facade.