When my son was born, breastfeeding was very difficult and ended sooner than we expected. As soon as he drank formula milk (based on cow's milk) he became a very sicky baby. We would go through 8 or so bibs a day, plus 4 or so full outfit changes, for baby, hubby, and me. Because he was our 1st, we thought all babies were like this. He started on cow's milk at one year, and has had lots of colds for a child his age.
At almost two when we had our next baby, who is breastfed, we realised he must have had an intolerance to formula milk, and thus cow's milk. We changed to goats' milk, and he is a changed boy. He is no longer constantly ill, and changing dirty nappies is much more pleasant, as he obviously digests goats milk much better.