@BlueSpruce, I'm sorry in my opinion but you are wrong.
A floor in any building is designed to carry its own load as well as the estimated maximum load to be placed upon the floor. Any individual floor is not designed to carry the weight of two, or more loaded floors. Many buildings, those included, would no doubt have to carry the load of banks of computers as well as other plant and equipment, desks and people. If a floor is overloaded beyond its designed capacity it will fail. I would imagine that there would be maximum stated loadings that can be stored on floors in high rise buildings.
Even with titanium beams these principles apply. It may be that the section size of titanium beams is different to steel but they will not be so large as to allow double or higher weight supporting capabilities. Titanium and steel have different properties but titanium will only be used as a substitute where design dictates and costs allow.
In this scenario, from memory there were over 100 floors, so it is inconceivable that even one floor could support the weight of another dropping maybe ten or fifteen feet with the supporting steel, floor weight, walls, plant and equipment, plus people. The floor it drops onto is also bound to fail and so on. The only way to prevent collapse would be to have supporting walls, or propping from top to bottom which would probably be impractical and add too much costs.