Unless the lease grants greater rights, the Roommate Law (Real Property Law §235-f) allows a sole tenant who is party to a lease to have immediate family members, one roommate, and the dependent children of the roommate live in the premises.
Unless the lease grants greater rights, if two or more tenants are parties to a lease, immediate family members of the tenants are allowed, but no roommates are allowed, except if a tenant moves out. Then one roommate (and the roommate's dependent children) can take the place of each departing tenant. And at least one of the original tenants (or a tenant's spouse) has to occupy the premises as a primary residence.
Real Property Law §235-f(4):
Any lease or rental agreement for residential premises entered into by two or more tenants shall be construed to permit occupancy by tenants, immediate family of tenants, occupants and dependent children of occupants; provided that the total number of tenants and occupants, excluding occupants' dependent children, does not exceed the number of tenants specified in the current lease or rental agreement, and that at least one tenant or a tenants' spouse occupies the premises as his primary residence.
See §235-f in Real Property Law - Article 7.