I don't think you can even buy another ticket (in any class of service) if you're already booked on the same flight with same AA number. The system would likely cancel the new booking out anyway since there's already a paid, confirmed booking. And since your company's agency 'owns' the ticket, I guess AA won't just let you pay the fare difference to up-fare it? Or is there an option on aa.com to change it yourself?

We all moan about the lack of LPs for buy-ups. It is what it is. AA knows that it would probably be a revenue loss in the long run from those who do buy business class outright (which there are many). If those same customers knew they could get LPs buying the upgrade offer, they may just buy coach then buy up.