American Express Membership Rewards - Booked flights using AMEX Travel using points

I booked a flight using AMEX points and was booked into a low fare class which means I won't receive that many miles through my frequent flyer account. I want to book a higher fare class, can I call AMEX and have them refund the points for a moment as I purchase a higher fare class ticket on the AMEX travel site? If I have a platnium card, does this make a difference or is the policy strict throughout all cards? Help me. Thanks.

-Zak

Just out of curosity did you use MR "Your ticket" or Membership Reward points to purchase. Either way it stinks.