Well if you were stopping over in either HKG or SIN (meaning longer than 24hrs in either) then for sure that would be invalid because it is then no longer "a transit without stopover".

Kiwi Flyer says he's managed to do what you are planning, which surprises me because I don't see two transits constituting "a transit without stopover" I tried doing it in the on-line tool and it disallows it. But this might be a case of YMMV if you try it via an agent or an airline