A leading preservation group hopes to save an iconic 1920s Star Island house from demolition by having it designated a historic landmark.

In an application submitted Wednesday, the Miami Design Preservation League asked Miami Beach’s Historic Preservation Board to consider designating 42 Star Island Dr. a historic site in order to protect it from its current owners, Dr. Leonard Hochstein and his wife Lisa Hochstein, one of the cast members of Bravo’s Real Housewives of Miami.

“It’s loss would be like knocking a tooth out of the Mona Lisa,” said Mike Kinerk, who signed the application as the league’s chairman pro tempore.

Reached Thursday morning, Hochstein, a plastic surgeon, called the designation attempt a publicity stunt.

“These people are misguided,” he said. “I don’t know what it is about their personalities that they feel they can dictate to others what they can do to their homes.”

The Hochsteins have been a lightning rod for criticism — some of it mocking — since an engineer they hired said the existing 1925 home on the southeast corner of ultra-exclusive Star Island was beyond salvageable and the couple filed to raze the building and build a 20,000-square-foot estate. They said they bought the home at a foreclosure auction for $7.6 million and now want to build a six-bedroom, seven-bath mansion with a home theater, game room, and wine cellar, as well as a five-car garage and a guest house.

Preservationists, horrified at the idea of losing a prominently located home that represents the 1920s boom and was designed by notable Miami architect Walter DeGarmo, started an online petition to save the home. Design and real estate blogs also ridiculed the couple’s proposed new home design and existing Sunset Island home, deriding both homes as gaudy and oversized.

And the issue has touched off a debate about Miami Beach’s preservation efforts.

Current laws have set up historic districts and protected scores of buildings, such as Ocean Drive’s iconic Art Deco hotels.

But property owners who want to raze homes built before 1942 that are “architecturally significant” but not historic need only have the city’s Design Review Board approve of a new home design. And while the city has a policy that allows third parties to request historic designation for homes, it heavily favors property owners in cases where there is a dispute.

Still, Kinerk said Thursday that the threat of losing the DeGarmo Star Island home has energized efforts to save single-family homes.

“We will be moving to designate all important houses in the city,” he said.

And at the urging of activists, Miami Beach commissioners also agreed last week to begin discussing new preservation legislation.

Meanwhile, the Hochsteins still need to win the necessary approval of Miami Beach’s Design Review Board in order to build what they have called their dream home. Earlier this month, Planning Department staff said a structural analysis of the home needed more work, as did design plans for a new home. They urged the Hochsteins to consider implementing elements of the existing house in their planned estate.

A second hearing is scheduled for Feb. 5.

A hearing about the home’s historic value is scheduled for one week later. That issue would be “moot” if the city’s Design Review Board approves of the Hochstein’s demolition plans, said their attorney Michael Larkin.

However, the ruling could be appealed to the Miami Beach City Commission.

“This is pretty ridiculous,” said Hochstein. “If they had designated this home I wouldn’t have bought it. It’s all after-the-fact, and it seems wrong.”