You can't get a new EAD
Didn't your school's International Students office talk to you about OPT? OPT - Optional Practical Training - is available for just one year of full time work for each level of education that you do in the US in college. That means you get one year for an undergrad degree, one year for a masters, and one for a PhD. So unless you get a graduate degree at this point, you can't get more time to work on OPT, even then only after you complete the degree. So the short of it is, no, you can't extend your OPT EAD. Your status in the country is non resident alien unless you change to an H1 visa or something else. But if you move to an H1 visa, you won't need an EAD to work as the visa itself lets you work. You can get an EAD if you have applied for Adjustment Of Status to a resident for GC. That EAD can be extended for as long as your application for AOS is pending.