For a options TS can consider:
1)Air Passes offered by alliances as mentioned by
DealuxTravel. Best option for multiple cities plus direct / non-stop flights. However, pricing might not be cheap. If it is within the same country, there is also like China Air Pass or Japan Air Pass.
2) Redemption of miles can also offer such multi carrier arrangements, albeit with only maximum 1 stopover (for saver award on KF miles). Like you can do a round-trip to NRT, with a stopover in PEK and able to choose most star alliance carrier, so it can be SQ for SIN - NRT, then CA for NRT - PEK, then SQ for PEK - SIN.
3) Another option would be for a carrier that is able fly to all your destinations, like SIN - HKG - NRT - HKG - SIN on CX, though that will involve having a transit in HKG for one of the trips between SIN and NRT.
4) Last option will involve circumventing the minimum stay rule. You can also nest round trip tickets. For example, you can buy 1 round trip for SIN - HKG - SIN, then buy another round trip on the same or another carrier for HKG - NRT - HKG. This option would also involve the additional transit for at one of the flights between SIN and NRT plus the possible hassle of doing a transfer, if the two airlines do not do inter-line baggage.
That is because one way air ticket normally has full miles accumulation
Expensive round trip tickets also allow full miles accumulation. What's the link with miles accumulation and one way tickets being expensive? Rather, it is usually the other way around where expensive tickets, regardless if it is one way or round trip, will have full mileage accrual.
and it doesn't restrict the days you stay there. Return ticket normally has maximum days restriction.
To put in more in perspective, is that cheaper round trip tickets usually have minimum / maximum stay restrictions. While full fare ones will have no restrictions, though you would have to use it within its normally 1 year validity. And they are probably charging you for the full fare ticket or half of it.