The New York City Council is poised on Thursday to take a major step to address the city’s housing crisis by approving a plan that includes the most significant zoning changes in decades.

Its new rules could make way for 80,000 new homes over the next 15 years in a city where rents have soared and the vacancy rate is at its lowest level in half a century.

The plan is expected to pass the Council with a narrow majority, a sign of the contentious negotiations that have consumed City Hall for months.

Mayor Eric Adams, a Democrat, has made the plan, known as City of Yes, a top priority. His administration won over skeptical lawmakers by agreeing to spend an additional $5 billion on affordable housing and infrastructure projects and by scaling back some of the boldest proposals.

The goal is to build “a little more housing in every neighborhood” by changing rules around parking mandates for new construction and adding homes above stores and in basements. Opposition was fierce in neighborhoods in Staten Island and Queens that have many single-family homes, with residents objecting to the prospect of new high-rise apartments.

Mitchell L. Moss, a professor of urban policy at New York University, praised leaders for reaching a compromise and said that the city needed to build housing, especially near subway stations.