There’s quite a few youtube videos on competitive eaters who eat massive amounts in one sitting (i.e. Michael Phelps challenge, where you eat 12,000 calories). What does the body do with all that extra food?
It leaves body via one orifice or another.
Assuming it all stays down, it will pass through the digestive tract. Now, there is a limit to how much a body can process in a given time period and any excess beyond that will exit without being absorbed, although digestive juices will alter its appearance/texture/smell considerably…
In other words, shit happens? 
There is a chapter on this very subject in Gulp by Mary Roach - which is worth reading for many other reasons. IIRC the answer is nothing special. The stomach can expand by an amazing amount (and they’ve practiced expanding it) and the food just sits there until it gets eliminated. Some people are better at it than others.