Cross Bleed Starting
On the A300-B4 we start no. 2 from the APU and then start no.1 with cross bleed air. The bleed air pressure is sufficient at idle so we don't have any limitations as to when on pushback we start the other engine.
I used to jumpseat on DC8-73,s and they started no's 2 & 3 from external air and then push back. When pushback was complete the running engines were boosted to give 40 psi. to cross bleed start the other engines, so this had to be done clear of other aircraft.
It all depends on the aircraft or engine type.
Hope this helps.