Luxury carpet scion Steven Stark and his wife, Candice, are looking to part with their Park Avenue pile.

Mr. Stark, whose father founded upscale New York furnishings company Stark Carpet & Fabric in the 1930s, and Ms. Stark have owned the mansion-sized, five-bedroom spread on Park Avenue in Manhattan’s Lenox Hill neighborhood for more than a decade, during which they took the once-decrepit space down to the studs. It’s now an updated, contemporary home spanning 5,025 square feet at one of lauded architect J.E.R. Carpenter’s landmarked 1930s buildings. It hit the market on Tuesday asking $15.95 million with brokers Andrea Wernick of Warburg Realty and Suzan Kremer of Douglas Elliman.

The Starks bought the Park Avenue apartment in 2008 as an urban pied-a-terre away from their main house in New Jersey—though they’ve spared no expense in making the second home their own, Ms. Kremer said.

“It’s been meticulously redesigned,” she said.

In the market for a fixer-upper, the couple purchased the original unit from the estate of its previous owner, property records show, and set to work on an ambitious project that included breaking down walls and raising the ceilings to more than 10 feet, the agents said.

There was little to salvage from the former apartment, which had cardboard taped across old air conditioning infrastructure and peeling paint, the Starks recalled in a 2013 interview with Architectural Digest. They were not available to comment for this story.

They took down a wall that separated the formal living and dining rooms, raised the doorways to bring in more light and installed a sleek kitchen with white-glass countertops. The result was a modern, open feel that still had nods to traditional, pre-war architecture. The home is replete with custom millwork, pearlized Venetian plaster walls and has a library paneled in white rift oak, as well as two gas fireplaces.

The Starks, as empty nesters, had little need for the apartment’s original five bedrooms and instead created a three-bedroom, four-and-a-half bathroom layout. Their cozy media room could convert back into a fourth bedroom, while a sitting room in the main bedroom suite could serve as a fifth bedroom as needed, the agents said.

There’s also a rare area of outdoor space off of the living room, which the owners have surrounded in a privacy hedge of faux boxwood plantings.

Besides the aesthetics, the owners also replaced the mechanical systems, rewiring the electrical, updating the plumbing and adding triple-laminated windows to sound-proof the second-level unit form the bustle of Park Avenue, Ms. Wernick added.

The Starks’ eclectic mix of abstract art and sculpture add pops of color to an otherwise completely neutral base—a blank canvas for the next owners, the agents said.

“It would work with anyone’s taste,” Ms. Wernick said, adding that the buyers need only bring their toothbrush.

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