I think you can keep both open...
if you keep at least one CC in each one. You cannot have the same CC on both accounts though. When I first received my PC CC, I was already a member of the AA iDine program and tried to enter my PC CC but it kept telling it was already enrolled. I finally called iDine and that is when I found out PC had an iDine program. I still decided to stay in the AA club because building miles there is my top priority right now. You are best to call them and get the official word.