Tried BA.com chat this am to add BE number and this was the response.
I have checked this for you with my team. As per the information received, the business extra program is with American Airlines and you need to speak with them in regards with this to update.
I have verified and checked this with my team. twice. We do not have any special place to add the number. We can only add the frequent flyer number. As suggested by the team, I tried to update the same number there however, it says invalid number. I am really sorry however, just to let you know that I tried and I am sharing the correct information for you. I really want to help you.
Also tried calling BA and just got a ..we are too busy call back later message for both existing bookings and other questions.
Will have to try again or do on the back end. If any one has any other ideas, I am all ears