It is possible. I just tried to do it JFK-LHR-BLR-LHR-JFK with JFK-LHR-JFK credited to BA and LHR-BLR-LHR credited to AA. In my case it got screwed up with all sectors but BLR-LHR credited to BA.

After some long "discussions" with the BA people here is what I was told. The only way you can guarantee that the miles get posted correctly is:

(i) never have any mileage account AA/BA entered into the reservation or the flights electronically,

(ii) keep all your boarding passes and ticket receipts, and

(iii) follow instructions on BA and AA websites to credit missing miles retroacticely once you return.

I tried doing it "electronically" and have boarding passes with the correct mileage accounts clearly printed on them. Despite this the LHR-BLR segment was still credited to BA. Again, as silly as it sounds I was told the only way to "guarantee" correct crediting is to make sure no FF number ever touches the reservation and flights and then get credit "manually".