Like others here I have many times lifted the entire side of my car using only the front jack point on the rocker panel. And when up in the air, the door opens and closes just fine. Not much flex that I can see. No extra bracing.
Going back to the OP's question, I really don't think that "BMW feel" you're looking for is the result of chassis braces or extra rigidity. An e46 chassis is very "controllable" and the chassis is far flexier than our s197. You mention you have a 2005, unknown mileage, a lot of stuff could just be worn out after 13 years, plus a lot of dampers suck. So I would focus on replacing any worn bushings, front and rear control arms, sway bar links, PHB, etc., and then I would really focus on shocks, shocks, shocks. I don't know what comes on that coilover setup you have, but really good shocks are a huge difference maker. A lot of that "taut but supple" feel you get with BMWs I think is the result of excellent dampers. The digressive valving of good Bilstein monotubes is a real difference maker in this area.
Going back to the OP's question, I really don't think that "BMW feel" you're looking for is the result of chassis braces or extra rigidity. An e46 chassis is very "controllable" and the chassis is far flexier than our s197. You mention you have a 2005, unknown mileage, a lot of stuff could just be worn out after 13 years, plus a lot of dampers suck. So I would focus on replacing any worn bushings, front and rear control arms, sway bar links, PHB, etc., and then I would really focus on shocks, shocks, shocks. I don't know what comes on that coilover setup you have, but really good shocks are a huge difference maker. A lot of that "taut but supple" feel you get with BMWs I think is the result of excellent dampers. The digressive valving of good Bilstein monotubes is a real difference maker in this area.