Anyone know how or if I can book a multi city flight on American Air site and fly economy from Nashville to Chicago as an example, then business class to Europe, and then economy on the two returning flights home. The flight over is the one that is the one I would like to relax so business class is great but not needed on the other flights.
If you want to fly from Nashville to, say Paris, you would enter the information like you would want to take a round trip between those cities. Once the flights come up, select Business class for your outbound trip. Once you do this, the return trip options show up. You can select a coach return and the price will be reduced accordingly. When I looked at an example for Paris, the return in coach dropped the price by $1,995 and the total was $3,156. You will fly 1st class to Chicago, Business to Paris and then coach all the way home to Nashville.
If you're not able to do this on American's website, you may have to call them. Since it's business class for at least part of the trip, see if they will waive the telephone booking fee.
I did this on Delta when I lived in Nashville, but I did have to do it over the phone. Savings were minimal however so don't expect that BNA to ORD in coach to save you a lot