Yes you can: Q10. May a student eligible for a cap-gap extension of post-completion OPT employment authorization and F-1 status apply for a STEM OPT extension while he or she is in the cap-gap extension period? A10. Yes. However, such application may not be made once the cap-gap extension period is terminated (e.g., if the H-1B petition is rejected, denied, or revoked), and the student has entered the 60-day departure preparation period.