Originally Posted by Andy33

You shouldn't have visa issues, because AMS, FCO and MLA are all in the Schengen Area, and US citizens don't require a visa to enter the Schengen Area as tourists. The OP's problem was related to travelling between two places in the Schengen area via somewhere outside it, and so requiring a multiple entry visa.

However if your tickets back to the USA are on the same booking as the AMS-FCO and FCO-MLA flights you propose not to catch, you can have big problems of a different sort. Unless you get advance agreement from the airlines concerned, if you miss any of the sectors on a flight booking, all subsequent sectors are automatically cancelled.