Any student wishing to extend after the expiration of their Form I-20 or Form DS-2019 (i.e., date listed on #5 of the Form I-20 or #3 of the Form DS-2019) will be unable to do so as SEVIS automatically terminates your status. You will then need to apply to USCIS with a new visa document issued by the International Students & Scholars Office for a Reinstatement.
The reinstatement process is very risky and not always approved by USCIS. It also becomes a permanent part of your immigration record which could cause you problems when applying for future immigration benefits such as permanent residency, being approved for a security clearance, etc.
Please also remember that you must be maintaining full-time status at all times, so in order to ask to be reinstated you will need to prove that you have been maintaining full-time status and will need to include a copy of your transcript.
To request to an extension of your program dates, complete the Request to Extend Program of Study form
(pdf). Please return this form to the ISSO 60-90 days prior to the expiration date of your current Form I-20 or DS-2019.