Here are my results after experimenting just now with a reservation booked less than 24 hours ago:
Flight is for ATL-ORD-MAD-BRU-LHR-ORD-ATL (With IB/BA operated flights mixed in all with AA flight numbers)
ATL-ORD-ATL all have seats reserved on AA.com
Now, AA.com displays a primary PNR. Use that PNR to pull up the reservation on BA.com. Once logged in, BA will display a second set of PNR. Since BA and IB merged a while back, I'll assume they share a reservation system to a degree.
So with the second PNR obtained from BA.com, use that to pull up the reservation again on IB.com. None of this will allow you to reserve your seat unfortunately, but it will pull up all the information across all 3 websites.
If you get any further, please keep us posted. I have not called IB or AA regarding reserving seats on the remaining segment.