The de Blasio administration has good reason to want to protect mandatory inclusionary housing in New York, since it is expected to produce at least 12,000 below-market units of the 80,000 that the administration hopes to achieve over the next decade.

Indeed, in less than six months, nearly 1,800 units of affordable housing have been proposed through the program, including vast city-sponsored developments in the Bronx, a 1,500-unit redevelopment of the St. John’s terminal building in Manhattan (25 percent of which would be affordable), and even a hotel in the Rockaways, Queens, where housing could be built if the property were flipped.

So far, 38-42 West 18th Street, as the Adorama development is known, is not among them. Because the site is within the Ladies’ Mile Historic District, Acuity must build around the tenement and loft buildings, rather than demolish them. As an incentive for historic preservation, developers may seek permission to shift the air rights from older buildings to new ones.

Acuity wants to build a pair of towers reaching 170 and 185 feet; under the current zoning, the shorter tower, which is also narrower, would be capped at 60 feet.

Without the zoning permission, the developer could build only around 40 units. If Acuity were allowed to build its desired 62 apartments, some say it would qualify as “a significant increase in residential floor area,” which, as the new housing rules specify, is when they should take effect.

“I don’t care if it’s two units or 10 units; we want every affordable unit we can get in Manhattan,” said Gale A. Brewer, the Manhattan borough president. She said she was led to believe projects like this one would apply, “and now it feels like a bait and switch.”

Ms. Brewer, a Democrat, argues that without special permits like this one prompting affordable housing requirements, there will continue to be a lack of new apartments for working- and middle-class New Yorkers in much of Manhattan.