What vasantn does is precisely what I do: use two browsers and have the old res visible while pricing out the new res. As soon as you select flights on the new res, cancel the old one.

As others have noted, I have seen that AA no longer "dings" you immediately for having a duplicate res. I've been able to book the same passenger on the same itinerary on the same dates without aa.com saying this was a duplicate of an existing reservation.