On 747-400, normally start 2 engines at a time on every flight using autostart. For very hot days (say above 40C ish) or high elevation airports (NBO, MEX, etc), I would start the first 2 engines one at a time, then the last 2 together. And there is a Boeing bulletin about turning all packs off if the APU is older/high cycle to help out, but normally, you can leave one pack running.
As mentioned above, -400 has a better APU than the Classic, so 2 at a time is not a problem under most conditions. But after seeing slow starts or watching autostart cycle the fuel on and off under hot or high conditions, I now start the first 2 one at a time under those conditions (with all packs off), to help keep temperatures down and to get a quicker start. Then for the last 2 engines, you have the APU air plus the bleed air from the from 2 operating engines to help out.
Have been told you can start all 4 at once, but doubt it will really work. Autostart would attempt it, but as duct psi dropped, it would probably only start 3 at once, then get the 4th one running after one other engine had finished the start cycle and reduced bleed air requirements.