It happens, but it's rare. And there has to be a good reason. The request will be denied if the target school is at capacity.

New requests may be submitted for Child Care Hardship (K-6), Child of FCPS Employee, Medical, Emotional, or Social Adjustment, Resident on Military Installation, Senior Status, Sibling at Requested School

https://www.fcps.edu/registration/student-transfer-information

I know families that pay to send their children to Falls Church City Schools, so maybe you pay if attending another district.