I know it's possible to book AA coded flights by calling up the BA line - handy for trips to the USA to get the First class TPs.

I was wondering therefore whether it's possible to book other OW flight numbers on the phone? I've getting a cheap price for a WT ticket with a few legs when checking on ITA matrix, but I'm struggling to book it. AA site won't show me AY flight codes, and although I can sometimes get it to work on the Finnair site, it's not very good and is struggling with the level of layover manipulation I want to perform.

Just wondering what people's experiences were, and likewise for IB codes too.