Celestar340,
Thanks for the suggestion. I read it just before I left here to start the RTW trip. Splitting PNR -- I should have thought about it! After reading your post, I was tempted to do it but I didn't do it, because I didn't have much time and I also feared that I could lose the seats booked on the flights after the IB sectors. You know, if you cancel a part of the itinerary, what follows is usually cancelled as well. Am I right? Thanks, anyway.
I did fly the three IB segments over the weekend. I did not register any account number for the first flight on Sat., for I thought it might override the remaining two as Celestar340 said.
On Sun., however, when I checked in for the two remaining sectors, I asked the agent to register CP and BA account numbers. And she SAID she did it, without any problem. These numbers didn't show on the boarding passes and I asked her if the numbers were really registered, she double-checked them on the computer screen and she said they were registered .... I am not sure if that is true. But I have to see what will happen to my account statements.
IB was really something. AA, CP and BA all accepted different account numbers and they all appeared as per requested on the boarding passes.