Can a 2 engines plane takeoff at MTOW when 1 engine quits,or only at lower weight?

[john_tullamarine]

flying Mr Boeing's Tri-motor,

A gentleman's flying machine ..

There was a weight correction for "train on track"

And, in the same vein, one sometimes sees allowances made for transitory vehicles on roads and mast heights for itinerant vessels minding their own business in the waterways beyond runway head ..