As you can see, the pyramid will descend into the room. Therefore I must get rid of everything under the roof, marked in red here:
The problem is the area marked in blue. I'm not able to create anything like that, since all sides are sloping in some way.
It doesn't help if you bisect it in two, because you still have two sides sloping in the resulting section, and walls can only have one side out of four sloping.