New York University isn’t just gobbling up space in Greenwich Village. The university plans to spend $500 million on an expansion in Downtown Brooklyn. NYU President Andrew Hamilton said the 10-year plan includes adding 500,000 square feet to the school’s Tandon School of Engineering by renovating the MTA’s former headquarters at 370 Jay Street. That project will nearly double NYU’s 600,000-square-foot footprint in the area.