Gumboot, it is possible to answer your question in a simple way, using only F=ma, if you make lots of simplifying assumptions. Let's start with your already simplified case of simply dropping the upper 1/5 of the tower through 1 storey of open air onto the lower tower.
In order for the lower portion of the tower to arrest the collapse, the upper portion of the tower, already in motion, now has to stop moving. (Even if it were possible for it to "topple to the side" at that point, its vertical motion still has to stop or else it will keep smashing downward through the lower tower instead.)
To go from falling to at-rest, the moving mass must accelerate upward. The structure it falls onto must provide sufficient force for a sufficient amount of time to accelerate the moving mass to zero downward velocity. A lot of force over a short time will do, or a lesser force over a longer time.
How much time does the lower structure have to decelerate the upper mass? Actually that's not quite the right question yet. Let's look at the moment the masses come in contact. The lower mass starts resisting, and the upper mass starts decelerating. But it can't decelerate instantly, that would take infinite force. So the upper mass is still moving after it comes in contact with the lower. The greater the resistive force, the faster the moving mass will accelerate (slow down), and the less distance it will therefore move before it comes to rest. If the resistive force is less, the moving mass will accelerate to zero over a greater distance. (If the resistive force is less than or equal to the gravitational force acting on the falling mass (that is to say, its weight), the moving mass won't slow down at all, it will keep going and possibly accelerating downward. But we expect the resistive force to be greater than the falling mass's weight, because the lower tower was designed to support that weight.)
But as long as the upper mass is still moving, the lower structure that's providing the force to slow it down is also being deformed by that movement. That deformation is going to weaken the lower structure, reducing the force with which it acts against the moving upper mass. So we can transform the question of how much time does it take for the lower structure to bring the upper portion to rest, into over what distance (amount of deformation) can the resistive force continue to act upon the upper mass? This is where it gets complicated, because different kinds of deformation (buckling, fracturing, etc.) will affect the resistance in different ways over different amounts of time and distances. But we can look at ultra-simplified models of this.
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