Engine out performance
 

I have two questions. 1. I get into some "interesting " discussions when I suggest that continuing a TO after an E/O below V2 is sometimes (emphasis on somtimes) the safer course of action, What do you think? 2. Based on my first question, Am I correct in assuming that unless published, i.e. HKG, a SID will provide obstacle clearance with an eng out, assuming climb performance FT/NM is met etc. However, using T/O Analysis based on balanced field computations considers all of that. I am a 744 Captain and am referring to a 4 engine a/c. Am I right?

SID dont care how many engines you got...its a fixed gradient(3.3 or more as published )starting from DER which you shall not go below.
SIDs dont have acceleration gradient and do not assure engine out obstacle clearance requirements are met.
If Engine out follow EOSID or runway track to MSA...

Have you mixed V2 with V1? Aborting near V2 would be crazy?

Typically, the debate that occurs about aborting is the question of whether one should always "GO" above V1; there are some very special scenarios where above V1, although the standard practice is to continue, and that's how the training is usually done, there could be scenarios where stopping on the runway above V1 is a better course of action.

But the idea of continuing below V1 (assuming you have mixed up V1 and V2) is a very different one. You're potentially looking at a scenario where the aircraft is below the VMCG speed, which means that if you keep going with takeoff power on the working engines, there's no guarantee that you can continue to track the centreline.

I think you'd need to have a very very good understanding of the real VMCG margins on your aircraft, and the margin from the scheduled speeds to the (real) VMCG, to consider continuing an OEI takeoff at speeds potentially below VMCG. And I'd suggest that most crews do not have (and could not have0 that level of understanding of the underlying design.