In 1964 a SS was a trim option just like an Impala, was different from a Caprice which differed from a Biscayne, or a Bel Air. All where trim levels and had no affect what so ever on what occurred under the hood. So you could order a 153 cubic inch fire breathing four cylinder for your 1964 SS if you wanted to.
The only full size cars were having an SS makes any difference is on the "427 SS'' Impala or Biscayne or Bel Air as that wasn't a trim offering but a package from the factory that bought you a 427 big block motor, heavy duty suspension, heavy duty cooling, a TH400 or a Muncie four speed manual, a special blistered hood, special 427 badges, and the rest of the SS trim package that was offered that year : and the 1994-'96 SS Impala which once again was a performance package and not a trim package. I believe that you could only get the 409 horsepower 409 unless you also ordered the SS package with it, but that the SS package didn't include anything else being heavy duty with it, so you could get it with a three speed or a PowerGlide, with all standard suspension.
Chevelle, Camaro and the 1968-'72 Nova's all had a package that included heavy duty everything when you ordered a SS with a high horsepower motor that was only available with the SS package. On these "Muscle Cars" as they came to be known buying an SS package meant you where buying a factory prepped hot rod that you got in drove to the track (because no one would race on the street back then). The SS package at that time in automotive history on those cars meant performance not trim, marketing guys have been trading on that ever since on pick-up and full size luxury yachts by labeling them SS with a package of decals.
If you want a high performance full size car buy an old police car (the 9C1 RPO option code on the order form) and stick a high horsepower motor under the hood to compliment the super duty suspension, and heavy duty cooling, and heavy duty electrical wiring, and the posi rear end containing taller than normal gears in the differential. You could always add a SS package by upgrading the trim after the fact or do like I do and drive it as a sleeper that no one suspects can do anything as it is an atypical hot rod, that isn't painted red, or has a loud exhaust that screams "hey look at me"
There is a difference between form and function. I prefer functionality over anything else and let the looks fall where they may. My race cars do not look like race cars they perform like race cars. Often folks get it backwards and strive to look like a race car and think by adding a lot of chrome it will make it perform like one.