What kind of everything plan? If it is an everything data plan and you haven't been late on any payments then you are premier. Basically you have to pay them $99.99 a month on a family plan or $69.99 a month on a single plan for six months as a new subscriber or three months as an existing subscriber switching to a qualifying plan.
But to answer your question, no you cannot call in and be moved to Premier. The system does it automatically. If you should be Premier and are not, they can "fix the glitch" that is causing the problem but cannot move you to Premier directly.