My wife had problems doing what you have in mind - she checked in on-line for the whole journey on the BA and CX sites, but could only print her BA boarding card for EDI - LHR, it was impossible to get her CX boarding card. At EDI, we went to the BA desk to see if they could print her CX boarding card, but they told us that they couldn't do so because she had already checked in on-line....Apparently if she had checked in directly at EDI at the airport, she could have got both boarding cards. As a result, she had to get her CX boarding card on arrival at LHR.