We have recently been practising in the simulator heavyweight takeoffs losing one engine, then the other during the clean up. You have to jettison fuel to landing weight or below, but you can still continue climbing, albeit slowly. 2-engine out approaches are no problem at landing weight or below, nor go-arounds on 2.
To lose 2 at heavyweight/slowspeed before you have started cleaning up is probably pushing your luck too far- I don't think you could accelerate to start retracting flap without losing height, which you haven't got.