formula fed baby

Hi, my baby is 9 weeks old and weighs around 5.2kg. I have been feeding him 110 to 120ml formula milk 8 times a day. Most days, he takes very short naps (less than 30 min) in the daytime but can sleep at night with 2 feeds. Sometimes, i feel that he can drink more after 120ml. Should a 9 week old baby be sleeping in the daytime after he is full from drinking milk? I am wondering if my baby is not full thus cannot nap well in the day. If i increase the milk intake, will he drink more in the day and sleep through the night?