You should easily be able to do this if you call at 330 days out. But AA doesn't fly to Naples, so you would either have to get yourself to Rome (not that hard by train) or fly on BA. Last year, we did AA from DFW to LGW then BA from LGW to NAP. It was really easy. Now that AA does fly into LGW (BOOO), it would require changing airports in London, which I avoid at all costs.
I would try to do DFW-JFK-Milan (sorry, don't know its code) on the way over on AA and FCO-JFK/ORD-DFW on the way back on AA. But keep the BA intraEurope option in mind as well. Or you could even do AA to Brussels then Brussels airlines to Italy. There is more than one way to skin a cat, so to speak. (Not that I would ever skin a cat except in anatormy class--I love cats!)