Can I change schools while renewing my work permit in Thailand?

If you change employer you must change from work permit. Next to this if you stay inside Thailand on an Extension of Stay this must be cancelled on the last day of your work at old employer together with the cancellation of the old Work Permit. If you stay on a Visa that has the name of the school on it, than this visa can not be used to work at a new employer and you must get a new visa

The school will have to be listed in the work permit. You can work at a second job (school) but if switching from one to another you will need to take documents from the old school to immigration. Others should be able to clarify further