BA started quoting different rules for different sectors a few years ago. I asked an agent about this when I spoke to him on the phone. He confirmed that the most restrictive rule override no longer applies.

The reason I asked was that I was booking DOH-LHR-DXB in I class. As an inter-country open jaw fare rules were different for each sector. DOH-LHR was changeable and "refundable", LHR-DXB was not.

This is most useful for changes. If you want to change a changeable sector you can. Refunds however are a slightly different kettle of fish. You can get a refund, but the one way portion of the ticket will be deducted. For most fares this will effectively result in the refund's value being negative (i.e. zero).

I must add that this is merely my understanding since I have never actually requested a change to a multi-rule booking myself.