New York University is proposing the largest expansion in its history, with a new tower on Bleecker Street and three million square feet of new classrooms, dormitories and offices in the Greenwich Village area. The plans also call for creating a new engineering school in Brooklyn and a satellite campus on Governors Island, complete with dorms and faculty housing.

The projects, which would expand N.Y.U.’s physical plant by 40 percent over the next 20 years, are aimed at accommodating a growing student body and competing for money and prestige with other universities. They will require approvals from city agencies and have already met with a skeptical response from some neighbors and preservationists.

The city’s top economic development official, Deputy Mayor Robert C. Lieber, said that approval of the university’s plans was not guaranteed. “They’ve been deliberate and thoughtful,” Mr. Lieber said. “That doesn’t mean it’s all going to go exactly as they intended. There’s lots of opportunity for discussion here.”

The university has clashed repeatedly with its neighbors over much less ambitious expansion efforts of recent decades. N.Y.U. officials acknowledged on Monday that these earlier projects had been marked by piecemeal planning and undistinguished design and said they have made a concerted effort this time to conduct an open public process that is mindful of the neighborhood context, architectural quality and residents’ interests.