These big boats were designed to have a living room sofa soft ride. They wallow in corners and nose dive when braking. The stock spring rate is less than half of the inch pound rate of any Mustang or Camaro, shocks are valved to dampen rebound by the third or fourth bounce and as mentioned few have even a front sway bar never mind a rear one.
There were two suspension packages that where offered on the sales order form when the car was ordered. F40 was a heavy duty suspension that added a front sway bar and stiffer springs to tow a trailer or carry bags of salt in the trunk if you lived out side of the city and drove during the winter. The other suspension RPO was an F41 which on a Chevelle SS or a Camaro SS was part of the SS package to stiffen up your stock suspension and in the case of the Camaro with a Brake upgrade allow you to race your car in sanctioned TransAm events. Since the SS package on the Impala was style only (all show no go) a F41 is a rare find. F40 was found under all police cars, taxi's and many station wagons (if you are trying to source parts used).
The aftermarket doesn't offer a RPO F41 kit, but does offer a number of upgrades to improve handling. Fully boxed rear trailing arms with adjustable uppers is one part that removes flexing and twisting under load and rids you of a set of rubber bushings since they use either plastic or solid steel bushings. Up front you can go with tubular A-arms. At this point you can make a decision to retain the stock divorced coil and shock or combine the two into a fully adjustable coil over.
The advantages of a coil over are single (or double adjustable) shocks, with a threaded exterior body that allows you to fine tune ride height as much as an inch and a quarter (though you are supposed to buy your shocks by free ride height and amount of suspension travel desired; and leave the adjusting rings to fine tune the suspension with preload. If you retain the stock coils changing spring ride height involves taking the front end apart as opposed to just changing a shock with only two nuts.
A BBC car had a different free height on the spring than the SBC car did, but used the same spring rate. The actual free height was determined by the weight on that corner so an A/C equipped car would have a different length spring than a car with no power accessories at all. In the Chassis Service manual you can find reference to the weight each accessory added to the car over the base dry weight used in shipping (curb weight). You could look at the base weight and add or subtract the options your car had to obtain a weight to order a replacement spring or just drive the car to a truck scale and weigh it. With you in the car drive half way onto the scale stopping about mid dash to get the center of gravity. You would then half the front weight to get each corner. Drive off the scale on the other side once again with the car sitting half on half off the scale with the edge of the scale at the dash.
Bigger is better on roll bars, but they add weight, so if you are going really big many companies offer hollow roll bars to shed a few pounds. Weight is on the opposite side of Newton's Second Law equation that relates engine power and the weight of the car and acceleration (F=ma). Bigger tires and wheels really help performance but your car's body may not accept too big of a wheel and tire combination.
Finally with great power comes the need for better brakes. This car was designed back in the early sixties when the average road speed was only 45 mph. The Corvette didn't get disc brakes until 1965, and it was used in road racing at speeds three times faster than the full size car was expected to see. Since the Corvette shared suspension parts with the big car many parts interchange.