1. How do I form a corporation? 2. How do I form a nonprofit corporation?Yes you can run a company without an executive director or CEO. Many small companies do not have these two designations. Search our website for available business names and resources to help you through the filing process. Korn Ferry's recruiters in Scottsdale know the local market like no other firm. With innovative search methods, we uncover top talent in the market. Some discussions are appropriately held just among the board members—without the CEO. Illustration of a person looking at a board filled with notes. They can still have a Board of Directors as well, but it is not required.