As c-w-s mentions, this is normal on multi-itinerary trips (and the shadow Amadeus references that appear on BA are still different from the "relate" code on each of the US airline, so you could end up having 5-6 PNR references associated with your flights albeit on different systems).

While there is indeed nothing to worry about from that point of view, note that this system can lead to issues especially as the BA shadow reservations tend not to include the entirety of the itinerary each time. One thing is that you can only do seat assignments on the various segments on individual itineraries (ie there isn't typically a single on where you'll be able to assign seats on all flights) and this is where things can be messed up. In one recent case, BA "lost" our seat assignments on both an AY flight and a BA flight as a result and gave us rubbish seats instead.