E-verify and OPT

Im OPT in MBA field (not STEM) and living in VA. Can I legally work for a non e-verified company. I think I can but my DSO seems like they want me to find a new company that has e-verify. I have just 2 weeks left before my unemployed date be expired.

You need E-Verify for STEM OPT Extension. There is no such requirement for general OPT, but many recommend it.
Read Am I required to participate in E-Verify in order to hire F-1 students who seek a STEM OPT extension?