You may try, but no comment on probability of success
1 Case I know for your reference: SPR, MSc and BSc(Hons) from NUS, mid-career, applied to MOE to teach Eng Subjects or Chinese Language at Secondary School/JC, offered to teach Chinese at Primary School.
Heard that most, if not all China Passport holders are only offered to teach Chinese at Primary School, regardless of background.
MOE official answer is that subject/school level can be appealled, subject to approval.