So you'd be looking for something like:
BRU-CHI-MIA-LAS-LAX(stopover)-HND-PEK-HKG(stopover)-HYD-surface segment-HYD-DXB-LHR(stopover)-BRU
BRU-ORD-MIA-LAS-xLAX-NRT-PEK-xHKG-DEL-xHKG/xAMM-DXB-xLHR-BRU
also remember that there's a further restriction of 2 stopovers in the continent of origin (I believe 1 in each direction). So Dubai stay uses up 1 of the 2 allowed stopovers.
If you really need to fly into / outof HND instead of NRT then you'll need to adjust your port of departure from the US.