A friend of mine took off in a Citation 500 with a bad starter/generator with one engine in Mexico to get it back empty so since the failure was at the ramp his vmcg was zero. Of coarse max power had to be delayed until he wasn't using full rudder to keep it straight. With a very long runway most any procedure will work One guy forgot the flaps on a 737 but still had an uneventful takeoff except for a slight stick shaker at rotation.
I was given a stall recovery lesson in a Falcon 20 and the instructor failed an engine when I went max power so I reduced power on the good engine to maintain wings level and it upset him I didn't crash. We didn't have to repeat it to prove his point though. Most of the time a little common sense and long runways can get you out of most anything whether it is legal or not.