Cow’s milk is a great drink for little cows and older humans, but it just doesn’t have the right mix of nutrients for human babies. It contains more salt (much more) and protein than breast milk or commercial formula, and these excesses put a strain on young kidneys. It is also lacking in iron.
The composition of Cow’s milk varies from that of breast milk (and formula) in a variety of other ways, too. In addition, it causes mild intestinal bleeding in a small percentage of infants.
So if you’re planning to supplement, use either expressed breast milk or a formula recommended by the doctor—until your baby is a year old.