Done at Airlines of Tasmania when a Heron had a starter fail motor fail at YKII or YFLI, three engine take-off approved(crew only) approved in the ops manual.
Likewise National Jet, Southern did three engine ferries on the BAE-146.
I have seen photos of the demo pilots taking a BN-2 Islander off with one engine feathered at the start off the take-off roll.
The original Aerocommander was flown across the USA on one engine with the non operating engine prop removed and tied down in the cabin.