Partnerships for Affordability and Student Success Act This bill commits states to maintaining support for affordable higher education, and it authorizes federal-state partnerships to provide for higher education access, affordability, and completion. Specifically, the bill requires states to maintain support for institutions of higher education (IHEs) and for student financial aid at levels that are equal to or greater than the average levels of such support for the three most recent academic years. The bill also requires the Department of Education, after entering into an agreement with states, to award incentive grants to states to (1) provide grants to eligible students attending IHEs or participating in accredited study abroad programs, (2) reduce the cost of attendance at public IHEs, and (3) provide subgrants to eligible IHEs to reduce student costs and improve outcomes for students and graduates. Each state that receives such grant funds shall report annually on its progress in meeting its public postsecondary education goals and comprehensive plan for postsecondary education. Private, nonprofit IHEs may voluntarily elect to participate in a state's efforts under its comprehensive plan for postsecondary education.