yes, you can book it via phone but earlier just check routing/flights possiblity online, segment by segment. E.g. I think you could fly from PEK to HKG via ICN/GMP by OZ or TPE by BR. You can't do stopovers because this is the same region but you can do up to 23:55h layover
edit: if you really want to stay in plane much time... maybe PEK to HKG via TYO (NRT/HND) would be possible....however at least NRT-HKG by NH is on 763 and business class is not full flat.