You go to Venice for the water. That’s the whole point: the highly photogenic idiosyncrasy of an ancient city where everyone goes about much of their day-to-day lives in a floating fashion. “Everyone here wants a view of the water and it’s all about seeing the action,” says Michelangelo Ravagnan, founder of eponymous luxury real estate agency Ravagnan’s, whose own daily outings have recently revealed a surprise visitor.

“I was on my boat, taking a client to see a private island, when a dolphin emerged right next to us, in front of St. Mark’s Square,” says Ravagnan of the bottlenose beauty nicknamed Mimmo who—despite the hectic comings and goings of the many vaporetti, traghetti and gondole that ferry residents and tourists across the waterway—has taken up residence in the lagoon.

For humans who share Mimmo’s urge to be close to the Piazza San Marco—which is about 30 million of them every year, flocking to see such world-famous landmarks as the flamboyant 9th-century St. Mark’s Basilica, the Doge’s Palace and Venice’s tallest building, the Campanile di San Marco (St. Mark’s Bell Tower)—Ravagnan has a property unlike any other within his clutches. “This is the kind of property that a Venetian real estate agent dreams of handling for an entire lifetime,” he says, not a little breathlessly, of what is, without doubt, a rare opportunity in a world-class location.

The property in question—accessed out of sight of the tourist hordes, via a tiny backstreet—sits within another of the Piazza’s much-photographed historic buildings, the Procuratie Vecchie. This 12th-century building, remodeled in the 16th........

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