my doc told me give water if dehydrated, constipated, having bottles less than 2-3hrs apart or baby has white spots in mouth (which could be start of thrush.)
baby will take it if it wants it. you're not allowed to dd juice to it until 12weeks.
blake will happily take 2-4oz water most days. whereas if i up his milk he is sick. he's doing fine and putting on weight so docs n HV dont mind.