You can do it online - it will ask whether you want to break the journey with stopovers. (Being BA IT, when you say 'no stopover' on the way out it still wants you to put the date you want to continue, from the place you're not stopping over at!)
Give it a try - it helps to know when there is availability from something like SeatSpy - I tried it out departing on 11 Nov and returning on 17 Nov then 24 Nov from SIN. The issue will be availability and you will be particularly lucky if you can get the exact number of days you want in each place.