It would be much better for you to buy a round-trip ticket to Amsterdam, mosey on down to Rome and then get a cheap one-way ticket on a budget airline (e.g., Transavia) to fly back to Amsterdam for your return flight home. Or vice versa. Northwest and KLM as well as their biggest competitors occasionally have good sales to Amsterdam, and if you can arrange your own connection to New York, the Italian low-cost carrier, Eurofly, is the cheapest way to get to Rome, and they will most likely have a fall travel sale sometime late summer.

Better yet, since both Amsterdam and Rome tend to be among the most expensive destinations in Europe, consider alternative start and end points for your trip. You will have a better chance of finding a great deal to places like Cologne, Dusseldorf, Frankfurt, Munich, Geneva, and Milan, as well as cheaper connections among any of those cities, so you should at the very least include some or all of them when you check airfares.