You can pursue a green card once married. Your overstay will essentially be forgiven by USCIS. Assuming your marriage is entered in good faith, you will likely receive a green card. You will not be able to change or extend your status any other way. You can read more about adjustment of status at http://myattorneyusa.com/adjustment-of-immigration-status.
Answered on Jan 16th, 2017 at 4:09 AM