I’d prefer not to give you false hope here - the truth is that your personal spend represents very, very small change to BA. If it exceeded $1m they might be interested in starting a discussion with you. As it is, they’ll see that you’re already well wedded to BA and oneworld, so there really would be very little incentive for them to comp you, even if they did it within the alliance (which they don’t).

As has been said, if you have a very large company spend then try and leverage that. I’m guessing if you need a number for a local office that’s likely not the case though, because your company would already have a dedicated account manager.

I’d also caution against moving as well - as much as you might hate AA, if you’re US-based and can reach EXP there are considerable benefits in remaining with the FFP even if you fly on other metal. BA will not upgrade you very often, even as a GGL, whereas you have a fighting chance on an AA domestic.