Indeed, Ten Thousand will have enough amenities that residents won’t need to venture out if they don’t want to. The building will have boardrooms tenants can use for business meetings and a full bar for relaxation when the workday is done. Staffers will walk tenants’ dogs or pick up groceries.

Other perks for renters include the house Rolls-Royce, Bentley and Cadillac Escalade; a team of four butlers; and a wellness studio where doctors can be called on to inject Botox. An indoor lap pool has underwater speakers, and a private one-acre park features a chef’s kitchen, dog-run lawn and theater with an 84-inch screen and fire pit.

“There’s a bit of an amenities arms race, where each building wants to have the latest, greatest and newest features to outdo each other,” said Krishna Rao, an economist at real estate listings website StreetEasy.

Personalized Cake

Among Ten Thousand’s features are “predictive” technologies synced with residents’ iPads and smartphones that allow staffers to know when they might need to retrieve tenants’ vehicles, start brewing their lattes or surprise them with a personalized cake for a child’s birthday. The elevators will identify residents based on their key card or phone and automatically shuttle them to their floor, even making sure those with allergies don’t share a car with pets.

“Things will magically get done for you,” said Nikolay Tevekeliyski, the building’s general manager.

Developer Rick Caruso, whose 8500 Burton Way has even higher rents, said the biggest challenge for Ten Thousand will be getting its almost 300 units filled. The eight-story Burton Way building had just 86 units and a waiting list, enabling it to be fully occupied immediately after its 2012 opening, he said.

Luxury Shortage

But once Ten Thousand -- which has about 2,000 people on its “interest” list, according to Crescent Heights -- is fully occupied, it will be successful because there’s a shortage of luxury rentals, Caruso said. He said he hopes to build another luxury apartment tower too.

Rents at 8500 Burton Way, where residents’ average household income is almost $1 million, are in line with the most expensive buildings in Manhattan not attached to a luxury hotel. The median asking rent at the priciest such property, 456 Washington St., was $17,495, according to a StreetEasy analysis of active listings throughout this year. At 8500 Burton Way, the amenity list includes room service, dog walkers, grocery shoppers and access to a chauffeur and Mercedes-Benz S550 for trips to the airport or shopping.