Is it possible to over feed a breastfeeding baby?

Would be unusual. If you have a healthy supply of breast milk and baby is growing fast, it may seems that way. So, when baby is hungry, feed him/her. When he/she stops sucking, then stop. Regular follow-up with doc will help guide you how to ensure proper growth and development of your precious one. It is unusual to over feed a breastfed baby. Bottle-feed is a different story, as it is easy. Congrats and good luck.
Opinions vary. Those saying "no" state the weight baby accumulates will be shed once baby starts moving around & point out the many nutritional & immune benefits of breast milk. Those on the "yes" side say that weight gain accompanied by GI symptoms (reflux, gas, watery green bm's, abd pain) may be sign of overfeeding. Weight the benefits against the risks & choose for yourself.