It's a beautiful, seemingly on-family house abutting the Normandy. Can't figure out the address as it's covered by the scaffolding.

That's 349 West 86th. There was an ambitious plan for expanding upward in the late 80s:
http://www.nytimes.com/1989/12/24/realestate/postings-luxury-on-west-86th-a-russian-deal.html

Beat me to it! The next story in that search says the Normandy bought the air rights in 1999.

From what I found out, it's owned by a wall street type, and a lot of music videos are shot inside. Any more to the story?