Originally Posted by
Swanhunter
As noted above, you can MFU on AA flights but the fare classes required are quite restrictive.
Try to find a W fare. This is a mid-priced economy ticket on AA, though it was undoubtedly included since this is full-fare WT+ on BA. It'll still be expensive but typically far less than Y or B. You may have to call in order to do this, though.
According to AA's published fares, a W fare will be about 2.5x as expensive as the cheapest published fare for OP's dates/routes but only costs 1/4 of the full Y fare.
Also, will the BA system allow this to be done online on an AA flight when it isn't a codeshare? I know you can do it, just not sure if it can only be done through reservations.