I never recommend routine vitamins, as if it is not in breastmilk, human
babies don't need it.  The exception to this is tiny premies, who would not
have survived without technological intervention, they did not have the third
trimester in the womb to store up minerals and might need them.  The AAP no
longer recommends vitamins to nursing babies.  Supplemental iron interferes
with some of the important protective mechanisms in bm, as well as inhibiting
absorbtion of iron from breastmilk.  And guess who manufactures infant
vitamins?  If there is concern about vit D, there is always sunlight for mom
and baby.  In the rare case where an infant needs one vitamin or mineral, I
would like to see it supplied singly.
Take home message:  the levels of all nutrients in breastmilk are calibrated
to optimize the absorbtion of all the other nutrients.  Messing with this
balance without documented medical need can only be harmful.
My humble but well researched opinion.
Catherine Watson Genna, IBCLC