Definately worth asking them - my corporate TA is able to do this at my new place and I know colleagues do it quite frequently as some of our permitted fares aren't much cheaper than business class at times. It's done whilst they issue the ticket though - they route the equivalent charge to my employer and the balance to my personal card ( not after separately/within 24hrs )

Otherwise you may get offered a "POUG" during online check in (unlikely if its a connecting ticket though) or you can try buy an "AUP" at check in at the airport - plenty of threads around on here with indicative prices etc