i have a 4 door cherokee. if i were to remove all the doors, would i lose some torsional rigidity?

 

I think on the 96 and newer they added body stiffeners in the pillars and roof. Not sure though. Just don't remove the hatch, it does add stiffness

 

yes but only to the degree that the doors are wedged by the distorted door openings that result from a twisting structure. The loss = the ability of the doors to resist deformation. I have no idea how much that is but a cage could be designed overcome it by someone who knows how to actually calculate the value of the doors and the loads involved.

people take doors off all the time and like it, with and without a cage, but there is a structural impact.