Similar to WorkerBee's experience, I've done these bookings using the Multi-City function, which allows you to specify a date for each segment. It didn't require assistance. Actually I've never had to pay a fee for help when booking something that could not be done on line, but who knows these days.
I've done these stopover trips a number of times (NY-Budapest/open jaw/Prague-London w/stopover and then back to NY, etc.)
The AAdvantage desk agents, by the way, are some of their best and can be very helpful after you've booked. If you have to settle for an unsuitable booking, and are willing to keep checking, they can help you find other routing later. I had a route through Heathrow a couple of years ago; within a month they were able to find me choices through either Zurich or Madrid. As long as the begin and end points are the same, there's no charge.