In his April 13 veto of Senate Bill 4, Beshear said the legislation violates the state's constitution by attempting to control the boards of Louisville and Lexington's school districts.
Supporters say the law protects educators, while critics warn it could push vulnerable students out of the system.
Kentucky lawmakers passed two bills that will dramatically reshape leadership at Jefferson County Public Schools, putting every school board seat on the ballot and shifting more power to the superintendent.
At the elementary and middle school level, they can compete in certain state events. But that changes in high school.
A bill aimed at increasing financial transparency in school districts passed the Kentucky Senate.
The bill aims to enroll Kentucky in a federal school choice program initiated by President Donald Trump.
The Kentucky Supreme Court agreed to take a new look at its ruling over a law Jefferson County Public Schools argues is unconstitutional.
Qualifying cities would have to have a population of at least 5,000 people.