squeeze volume through wireframe shape

hi guys,

I created a quick tower using some rotation and scale (file attached) and want to squeeze a volume (for example a cube) through it. The lines should make room for the volume, but should stay on the original lofted shape.

I don't know if this is clear enough. the shape (loft) of the tower should stay the same, only the curves on the loft should move (make space for the cube).

thanks