At least that has been my experience on SQ 11 - (LAX-NRT-SIN) so basically same scenario, that when booking for a continous flight - meaning same day - it will not accept it as two bookings - however with the apporach of tiketing the follow on segment as open and making a seperate booking in the appropriate booking class for that segment it works out fine - some grief at check in though - but in the end you will have two BP - and of course at NRT you are met to be given a replacement for the second segment. The ways SQ works - bin there - done that - and that numerous times (BTW only once on SQ 1 though) works fine.

Cheers

Thomas