To add to the discussions above.
During a turnaround at an out station, if no APU or GPU available were available, the preference would be to leave engine #4 running. This is because pax entry/de-plane would normal be conducted through the left front and rear stairs. If fitted, his would be via the aircraft’s own steps. Great care and a full briefing to baggage loaders would be required, otherwise extra paperwork would follow.
In circumstances were no APU/GPU and engine 1 or 4 is kept running, a x-start procedure can be used to start the other engines.
Another reason that crews could find the APU not available on ground is airfield noise restrictions banning their use.
btw, there is also the dreaded DC battery cart ‘dark start’ procedure. But such talk is best left until Halloween…