My guess is that if its not up & running now, *A must be working on some sort of integration or at least cross-check to avoid members getting double/triple credit for flights.
In any event, I would not try getting multiple credit for flights, my guess is that the fine print you agree to when you sign up for these programs states that you forfeit all your miles if you (try) to pull off a fraudulent move like that... - I wonder what Counsellor would say to this.
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Gaucho100K