Faced with loss of thrust between Vr (198 KIAS) and Vzrc LG extended on 3 engines (205 KIAS), the last thing any pilot would reasonably consider would be to call for any engine to be shut down - particularly if the adjacent engine had also suffered a brief loss of thrust. In fact they seem to have acheived 205 KIAS and the captain subsequently ordered the landing gear to be raised. During the ensuing landing gear confusion and robbed of any available thrust from the No 2 engine, the speed fell below 205 and a positive climb gradient with Nos 1, 3 and 4 engines at contingency power would not have been acheived. The FO gave clear warning concerning the airspeed, but by then the aircraft was no longer able to climb, let alone accelerate to V2. Seeing a runway, the captain made a last and undeniably heroic effort to reach it; regrettably the aeroplane departed controlled flight before the runway could be reached.
No matter how damaged it might have been, if the No 2 engine was producing ANY thrust it should have been left running with all 4 throttles fully forward until Vzrc3le or even V2 was attained.