Well here's my 10 penneth worth.
Your take off brief covers what you plan to do in the event of a malfunction during take off. So fly or don't fly according to that brief. If you follow what you have trained and practised you have the best chance of a successfull outcome.
However
What we cater for in those briefings, among other things, is a single engine fire/failure. If you are unfortunate enough to suffer a multiple engine failure you are now outside the scope of your briefing so are not bound by it. Prior to V1 stop and all is well. Above V1 with the loss or significant damage to 2 engines on most occasions we are now talking about making the ensueing crash survivable. Best option here is in my view is to stop if you are still on the runway or just rotated and if fully airborne try to make it to water or flat open ground.
The problem with the above is diagnosing and reacting to the above in time to make the difference. In my 4 jet time I flew with the same crew day in day out and we had a crew SOP which was if someone shouted "multiple" on the flight deck we would stop if we still on the ground even if above V1 as the call meant 2 engines had gone and our preference was to take our chances off the end of the runway.
The Nimrod accidents at St Mawgan (bomb bay fire) and Kinloss (ditching with an uncontained fire) are 2 good examples of how a crew can use their experience to successfully handle an emergency not really catered for by SOP. The Nimrod accident at Kinloss (multiple birdstrike after takeoff) also shows what can happen when you lose 2 out of 4 engines heavyweight just after take off. Again the crew and fire services did a great job in makeing the crash survivable for all but the pilots.
All we can do day to day is cover the basics and hope that if we are unfortunate enough to be caught out by by numbers that our experience and training will help us through.
SSG. I, and I am sure many others here, find the manner of your posts disrespectfull and odious. In particular your assumption that airline crew are by and large unthinking automans is risable and contemptable. Personaly I come from a military background that included operational flying in fast jets, 4 jet, and 7 years of instructing. In the military we were taught to think for ourselves but also the key importance of following procedure and technique so that under pressure you make the right judgements. I have flown with many non mil commercial pilots and have the greatest respect for the vast majority and have learnt a great deal from them that has aided my successfull transition to commerial aviation. The majority are hard working and conscientious and eager to learn and improve. I have met very few unthinking automans. I am sad for you that you were unable to get the jobs you interviewed for but given the evidence of your posting here I am far from surprised. You have attitude/supervisory problem stamped all over you. Perhaps one day you will be ready but not until you learn a bit of humility and respect.