Originally Posted by onlySIA

If one leg as Saver + one leg as Advantage is fewer points than the combined route as Advantage (not necessarily the case, you will have to check the award charts) you might be able to do it by phoning up. It would require cancellation of your existing award (with cancellation fee) BUT I don't know whether agents can tell in advance whether a ticket will return to the redemption pool or whether the seat will be transferred to the revenue pool, and in any case the availability of segments as awards varies depending on the start and end points ("married segment" logic e.g. HND-SIN-LHR available but not SIN-LHR). I really doubt that phone agents have access to this level of information.

Short answer, it will be difficult and time consuming - possibly not worth the miles saved (you didn't say how many miles we're talking about here). And in the worst case scenario you get an incompetent agent who cancels your ticket and have to fight to get it reinstated, or you fall afoul of married segment logic and lose the ticket.