The New York City Council voted to permit New York University to add 1.9 million square feet to its Greenwich Village campus for classrooms, a gym and housing in the face of objections from residents and faculty who said it would change the character of the neighborhood.

Council members voted 44 to 1 to amend the area’s zoning and permit construction of four buildings after the university last week submitted a scaled-down plan with 20 percent less density than the 2.1 million-square-foot proposal the city Planning Commission approved in June.

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