If you want to upgrade with cash (i.e. pay the fare difference yourself) then you might actually be in luck. BA refuse to touch travel agent bookings, however AA are not quite so squeamish. If you call up AA and say you have an AA ticketed booking that you want to upfare, then you should be quoted the difference in published fare between Y and whatever you want to upgrade to.
I've only ever done this on pure AA metal, so I can't vouch for codeshares, but it's worth a shot if that's what you were hoping to achieve. Caveat emptor if your employer finds out you changed a flexible Y ticket for an inflexible I class ticket though!