They may have used to - but I sense there is some sort of resistance from the Agents these days.
As I indicated, it's been a real YMMV.
What I had done - and quite easily in the past was to take, say a LAX-xMEL-AKL after booking and moving the MEL-AKL out to link up with my 'next' one ex AKL as the date became available. More recently it has become difficult. (In the end I just used a DM 30K DM Business mile award to make the link for the last one.)
In any case, I will be trying to avoid making any further changes in my remaining JASA's.