Failed APU and airport doesn't have a GPU or ground air cart.
One engine can be kept running for ground operations.
Passenger loading would require the right engine. Cargo, the right for the top deck, left for the lower cargo compartments. Fueling would be another issue.
It's been done.
On the DC-10 and MD-11, the #2 can be kept running without interference to cargo, passenger, or fueling.