Possibly, but if it was built in full compliance with local zoning and building codes you might not have a claim. You should retain an attorney if you have not already, to see if you have any basis for nuisance, or other claims such as inverse condemnation.
The first step is to determine if he is in violation of the zoning law and if he complied with any conditions if he was given a variance. If there was a variance, were you notified properly? If there seems to be a basis to now object in a court, then bring all of this information to a land use attorney where you live and review the case and discuss any ideas the attorney may have.
If you found this "helpful" or "best answer," please click it with my appreciation. My response is for educational purposes and does not constitute legal advice nor creates an attorney client relationship which requires all the details and a personal conference.
I read the news account of the multiple dwelling in construction next to your property line, and as you acknowledged, the zoning in your neighborhood, allows for construction up to the property line.
New York City allows a lot owner near total use of every inch of the property, and in some cases, new buildings, are built abutting an existing building's "Lot Line Window."
See this article for a discussion on this subject:
If you have any hope of preventing the total loss of light and air to the 10 affected windows, you have to "halt" the construction and bring the neighbor into court. Perhaps your lawyer may discover that your property was better protected than the local zoning provided.
But you cannot continue to wring your hands about the harm done to you and not do something that may alter the construction of the new building. Stop delaying and hire an attorney.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.