Too much milk, if not balanced with other food nutrients, can lead to anemia and other nutritional deficiencies, believe it or not, because kids fill up on the milk which is lacking essential vitamins and minerals and too much can actually deplete iron stores. You say he is also a good eater, so that may not even be a concern. My pediatrician always said juice is unnecessary, to feed fruit instead, and only 1/4 cup a day juice max if we did give it. Jacy had a good idea of offering half as much in each cup. You may have to deal with some unpleasant attitude, but be clear and firm.