Hi Espada 3. Your suggestion is not impossible. I have done several 3 engine takeoffs for real on a 747. There was a special procedure for it, crew only and no passengers allowed. I have also done rejected landings on a twin jet simulator on one engine which involved touching down and putting full power on one engine at a speed of about 120 knots and it took off very easily.
I have also on a Boeing twin jet simulator tried doing a single engine takeoff. It is not that difficult. You cannot put on full power because you would lose directional control sideways. You have to start the takeoff roll by applying about 50% N1. As the speed increases and the rudder gains authority you can gently increase the power and once you get to V2 you can increase to full power. You use quite a bit more runway than usual. However Shiraz has an elevation of almost 5000 feet which would make the takeoff roll required much longer. You would never get authority from any Civil Aviation Authority to do a single engine takeoff in a twin jet which is why it is impossible. Theoretically though if someone experienced were to get in to the plane and steal it they could takeoff on one engine.
Incidentally as an aside I know someone who did a single engine engine takeoff in a Piper Navajo Chieftain at Jan Smuts airport in Johannesburg in the early 1980s. One engine had serious problems so was run at 900 rpm which was little more than zero thrust. The pilot used a lot more of the runway than he expected.
As for the Cessna 337 mentioned by a poster above. It is a central axis push-me-pull you type. When it first came out Cessna had a promotional picture showing it taking off with the front engine shut down. Several people tried it and there were a couple of accidents. I was once in a Cessna 337 and we shut down an engine in flight and could not restart it. We were disappointed to find it would not maintain altitude on one. No real problem as there were airfields nearby but I would never try to take off on one.