7 wk Still Seems Hungry

I am currently trying to create a freezer stash, for when I go back to work. Everything I've read suggests pumping after nursing until breast are empty. When I do this, my LO still seems hungry at the end of the next nursing session. Does anyone have any suggestions? Does pumping between 1-5a really help create a stash without messing with supply, I don't want to wake up just to pump if it's going to negatively affect his morning nursing session.