Legally, only the school you are are/going to teach could apply and give you the e2 visa (of course, the e2 visa is approve by korea immigration). Please check any e2 visa, the name of the school and the director or school representative is mentioned on it - by working with any other school not mentioned on your e2 visa, you are risking deportation and a hefty fine to re-enter korea. Please make sure that your e2 visa dates are valid, lots of troubles if your visa is expired.