When you start a new plan, the old one automaticaly cancels. You can not be billed for both. If your timing is off, you might send in a payment for the new one, and it could overlap the auto deduction for the old one. In that case, the old payment will be returned by way of a sort of negative deduction from your first check of the year. You do what whatever you're going to do and they pick up all the pieces for you.