Max takeoff weight is often defined as the max weight that you can takeoff and meet:
TO runway length (including the ability to safely stop from V1);
The ability to maintain a minimum defined climb rate and obstacle clearance if you loose an engine right at V1 while operating the engines within their certified limits;
Comply with structural limitations of the airframe.
The third of those is usually the least critical - in wartime (especially WWII), those first two are regularly abused. Heck, in peacetime, some less than scrupulous cargo operators will often abuse them.*
*Story told to me years ago when Boeing was discussing building a 1,000,000 pound MTOW 747F. Allegedly, when talking to a certain Asian freight operator, the operator responded to the effect 'So What, we've already done that.' At the time, the maximum available 747F MTOW was around 800,000 lbs.
