Maybe you can pay the difference to Premium Economy, and then try to upgrade into Business Class?

Very few airlines, if any, allow multi-class upgrades. But they all (for the most part) allow you to redeem miles for free travel in any class you want. What's that? You want to earn miles AND have a flat bed on the cheap? Sorry, can't have your cake and eat it too.

Also, some airlines will waive the change fee if you're only changing the class of service.