My baby is still hungry.

My preemie was supposed to be due on New Year's Day. He came into our lives on November 2. We have had him home now for a little over 3 weeks.  His pediatrician said that he needs to eat every 3 hours and no more than 3 oz.  I give him 3oz at every feeding. I can tell he is still hungry. I have a pediatrician appointment this coming Friday and will talk to his dr then. I feel bad not giving him more milk. Any advice.