On Miami Beach’s super-exclusive Star Island, a Real Housewife of Miami and her plastic-surgeon husband want to build a palatial mansion so lavish it might make a Roman emperor blush.

Only a splendid, if possibly rundown, Mediterranean manse by one of Miami’s great early architects stands in the way.

Now Dr. Leonard and Lisa Hochstein’s plans to tear down the 1925 house, designed by Walter DeGarmo, is blowing up into the latest row over the fate of a historic building in preservation-minded Miami Beach.

The imbroglio has put a spotlight on what critics say is a gaping hole in the Beach’s otherwise stringent preservation ordinance: Unlike other local cities with lots of historic and architecturally distinguished homes, including Coral Gables, the Beach lacks the power to designate an individual residence historic without its owner’s consent.

Beach residents and preservationists have launched a last-gasp petition drive to save the DeGarmo house, an iconic, whitewashed presence at 42 Star Island Dr. on the island’s southeast corner that’s visible from the MacArthur Causeway. People from as far away as Chicago have signed the petition.

Design and real-estate bloggers, meanwhile, have had a field day ridiculing what one, Curbed Miami’s Sean McCaughan, called the Hochstein’s proposed “real elephant of a house.’’ Dr. Hochstein in turn calls the criticism “nasty’’ and “offensive.’’

The bloggers are also going after the Hochsteins’ current Sunset Island No. 1 abode, now up for sale for upward of $10 million — a faux-Mediterranean custom job that Curbed Miami called “absolutely absurd’’ and The Real Estalker derided as “gaudy,’’ “meretricious’’ and “the house that boobs built.’’

“I think it’s a complete disregard for the historic house,’’ McCaughan said in an interview of the Hochstein’s proposed new home. “It’s obviously a huge slap in the face to historic preservation in Miami Beach.’’

Leonard Hochstein said in an interview that he and his wife had hoped to renovate the DeGarmo house, which they bought in a foreclosure auction for $7.6 million. The previous owner, since 1978, was Jeannette Branam, whose grandson was murdered along with his wife in the so-called “Joe Cool” boat hijacking off Florida in 2007. Branam was unsuccessful in fending off the foreclosure.

Hochstein said the house proved to be structurally unsound and unsafe because it sits well below the flood elevation level for the island.

He said he found bloggers’ snide references to his wife’s role in the Real Housewives of Miami reality cable-TV show and the criticism of his home design preferences misplaced, insisting the bayfront facade of the new Star Island house would not be appreciably different from the DeGarmo house from a distance.

“I can’t make everybody happy,’’ he said. “This is the United States, where we’re allowed, within reason, to build to your taste. If they don’t like it, they don’t have to come as a guest.’’

On Tuesday, the blueprints for the new Star Island house and the demolition request go to the city’s Design Review Board, which approves new construction. Because the house is not designated historic, the city’s famously strict preservation board has no say in the matter.