The project, named the Sexton Plan, proposes to add more than 6 million square feet to the NYU campus, much of it in Greenwich Village.
A public City Council hearing is planned for Friday morning, when opponents of the plan are expected to testify.
Earlier this month, the New York City Planning Commission voted in favor of the plan, which includes four high-rise buildings near Washington Square Park.
Many residents oppose the plan, saying it is out of scale with the neighborhood.
The 12-1 commission vote sent the plan to the City Council for approval.
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