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Is there a point in the climb out where if an engine fails IT WOULD BE SAFE to continue?
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Yes.
But you need to know your aircraft, your weight, the current atmospheric conditions and the field elevation.
And I don't know why everyone is saying at this point you need to make a "quick decision" - this decision should have been made before you taxied onto the runway!.
I use, and will teach, blueline is the decision for you. At blueline the gear comes up. Before blueline if an engine fails you land straight ahead regardless of runway available - you can use the standard "20 degrees off course" trick like singles do if there's a building, cliff, etc. that would make landing literally straight ahead dangerous - but the point is you land if your gear is down. If an engine fails after blueline (and the conditions permit) you continue to climb for a go around or continue at your present altitude to a "suitable landing area" - preferably a large flat field, or road, at a lower elevation than the airport.
But this is where knowing the conditions becomes important. If the density altitude, or the field elevation, is above your single engine ceiling you have to land because there is no way you can climb or sustain altitude on one engine. Your weight is important because the lighter you are the higher your SEC goes. The POH will have a way of determinig the SEC at given wieghts. Knowing the aircraft is important because the book may say it will perform but the only way to know if that specific aircraft will do what the book says is to spend time in it.
The key to flying a twin is knowing your outs and making your decisions ahead of time and then sticking to them. It does no good to say "before blueline I'm landing" and then actually doing something like trying for a continued climb.
Twins are no more inherently dangerous than a single, with one exception. Engine failure on takeoff. But you should have already gone through the situation in your head and know, ahead of time, what you're going to do if something goes bad.