As long as connections not too short then should be able to do this

DeltaFlyingProf, bags in that example would be checked through to HKG.

Eg LHR-SIN day 1 (on same ticket SIN-AKL day whatever more than 2)
separate ticket SIN-HKG day 1/2 (on same ticket HKG-SIN day whatever more than 2)