Do you really think one in Knoxville is enough?
I think the first one should be at the Campbell station road exit of I-40/I-75 (its just a few miles from the southern split) there are plenty of retail businesses there and it's still on the outside edge of the city/metro area, and putting one there services the Knoxville to Nashville route and the Knoxville to Chattanooga route.
But what about Knoxville to Lexington or Knoxville to Bristol or Knoxville to Asheville
You could move the single supercharger to a more central location like the I-40/I-640 junction but then it lengthens the trip required for the west (Nashville) and south (Chattanooga) legs. It also puts the supercharger well inside the city promoting local charging. It's also not as nice a part of town, not ideal in my book for several reasons.
So if you do multiples are you concerned with all 3 major routes out of Knoxville or just 2?
Another good spot would be east at the Strawberry Plains exit or Dandridge exit on I-40, well outside of the normal Knoxville city flow but has hotels/gas/etc at that exit. This feeds the routes to Bristol, Asheville, and Pigeon Forge/Gatlinburg (major tourist trap and gateway to the Great Smokey Mountains National Park).
Again another bad compromise would be to put one near the 40/640 junction on the east side but local charging and lesser value to the I-75 route makes this an even worse choice than on the west side of town.
I-75 north has dozens of exits that would be good for a supercharger, I guess I'd do Lake City exit on I-75. Keep it north of powell/halls which is overcrowded and would see much local charging. Lake city is right at the junction for oak ridge/clinton travelers coming up 25W.
So if I had the choice to cover the east TN area with 3 superchargers I'd do
I-40 exit 373 (campbell station rd)
I-40 exit 398 (strawberry plains pike) or exit 417 (dandridge / hwy 92)
I-75 exit 128/129 (Lake City)
of course you could split that out if you want more chargers and do
I-40 near crossville (between Knoxville and Nashville)
I-75 Athens (between Knoxville and Chattanooga)
I-40 exit 398 (strawberry plains pike) or exit 417 (dandridge / hwy 92)
I-75 exit 128/129 (Lake City)
with 4 superchargers you cover all the major routes out of Knoxville leaving only the south route to the smokeys (US 441) stuck on L2 only.
Given all that if I had to limit it to 2 superchargers I'd just do
I-40 exit 373 (campbell station rd)
I-75 exit 128/129 (Lake City)
as I feel the west, south, and north routes will get more traffic than the east and I guess the tourists going to Pigeon Forge / Gatlinburg would just have to L2 charge.
I can't imagine this area with only one supercharger in the eastern third of the state.