The measure sponsored by Republican Senate Majority Leader Mark Norris of Collierville unanimously passed the Senate Education Committee on Wednesday.
The proposal would lift a 1998 ban that forbids municipalities from starting their own school systems.
The measure would benefit six Memphis suburbs seeking to bypass a merger of the Shelby County and Memphis school districts and run their own schools.
The suburbs voted in August to create their own districts after the Legislature passed a narrowly crafted bill that allowed it.
Shelby County officials argued in court that the law violated the Tennessee Constitution because it applied to only one county. A federal judge agreed and struck it down.