The max takeoff weight in the book isn't the actual maximum. It's the "certified" maximum. Anything beyond that may cause structural issues during takeoff, but probably won't be that big of a problem until you land. You'll need to be especially creative on getting very low on fuel, so you don't crash through your landing gear.

Sure, there are hard laws of physics.

Until you get to those, you'd be surprised how far some creativity with weight distribution, getting rid of unneeded cargo or even plane parts, using stuff to your advantage, and a little daring to push the plane to its limits, goes...

Way beyond what the "by the book" pilot who isn't creative can achieve in times of need.