I think the answer is no, following what madrooster wrote and also these terms from the Frequent Flyer Terms and Conditions. It seems you have to stick to your routing and if you are lucky may at best be able to push the date of a particular segment (noting the point about a ticket not needing to be reissued)
14.7.6 Subject to this clause 14.7, the following changes are permitted to a Classic Flight Reward flight before departure of that flight, provided the booking contains one or more Flight Segments that are not within Australia, and the Flight Segment(s) being changed do not include a partner airline that requires a ticket to be reissued for the change. Any such change will incur a Change Fee (see the Fee Schedule) per passenger:
(a) change to flight number; and
(b) change to date of travel.
14.7.8 The following changes are not permitted to any Classic Flight Reward within 24 hours before departure from the point of origin of the first Flight Segment on the Itinerary:
(a) change to class of travel;
(b) change to any Segment routing or airline; and
(c) change to name (only for Flights with a Qantas (QF) flight number on the ticket that are operated by Qantas).
