I have an update and a "fix" for that Error Code: CP15079

After a lengthy online chat with a Singapore Airlines rep, he finally worked out that one of the segments from my multi-city itinerary (Tokyo-Singapore-Bali-Tokyo) was "not combinable (sic) with the other flights and it won’t push through the system here and probably that is the reason why you’re getting an error".

He identified which one, and after choosing a different time, I was able to book. It's not a proper fix, but that's the reason for the error message. It's very silly that flights that can't be combined are still displayed on their own website, but...

Hope this somehow helps!