Hi 62aClubWorld. I've managed to book more sectors with the AA multi city tool by picking city pairs there are no direct flights between. It is forced to give you additional sectors.
For example, assuming you were doing a standard TP run that seems quite popular amongst the TP runners, say DUB-LHR-MIA-LAX-HNL rtn, the six city pairs I would enter into aa.com would be DUB-LHR, LHR-MIA, and MIA-HNL and then the reverse to return. As there are no direct flights between MIA and HNL, it will display connecting flights, amongst which will be MIA-LAX and LAX-HNL.
In order to get the widest possible choice to match to your ita matrix itinerary, set the aa.com 'how do you want to search' option to 'schedule' and select 50 in the 'show flight results' drop down box.
Select fare preference as 'business class or higher', under 'carrier' choose 'American Airlines, American Eagle and oneworld' to get BA flight options and select your flights from the results given.
Hope that helps.
Happy New Year everyone!