In my experience, the company cannot extend an mel on its own authority, JAA airlines i used to work for the normal practice was the QA dept. would have to contact the NAA for authorisation to extend and MEL, and they need a bloody good reason to do it. The NAA i worked under were very restrictive granting extensions.
More often than not ythe aircraft was on a "no fix no fly" when the MEL expired. I suppose it depends on the realationship of the company with the NAA.
