How much would a roll cage stiffing a car up?

Alot. But .... I put in wolfe race craft through the floor subframe connectors at the same time I did my 8 point cage. The connectors probably helped a ton all on their own. Mines welded in. Don't put a cage unless you really need one. I don't need the one I have and have been concidering cutting it out. Make sure what ever you get is track legal. I have low slung door bars and is not legal. The cage has been more a pain in my a$$ than any thing. Plus if you ever crash and your not wearing a helmet or have the bars padded it can be more dangerous than not having one at all. Like being hit in the head with a pipe at 50mph.
 
I had a 6 point in my last Mustang and you could jack up one corner of the car and that whole side would lift up off the ground...it was STIFF.


Remember though, a stiffer chassis will only make a stock suspension even worse...you've gotta go for the whole package to really get anything out of it.