How does e-verify work for multiple location company?

I was just offered a job from a big company. My current EAD expires on december, and I am eligible for stem extension. The company has several branches in different states. But the branch I had applied in seems to be not e-verified. Can the company participate in e-verify now? I had looked up the state laws on e-verify and the particular state only requires companies to participate in e-verify through local and municipal laws. What does that mean? If the company has participated in e-verify in different state, will that work on other states too?

Read the USCIS FAQ- Multiple Sites Employer E-Verify