I poked at one recently, and one major problem is that the power supply sits right above the analog board, and spits out some terrible hash. Basically, you get every multiple of 60 Hz up to a MHz or so, and a pretty healthy pile of it. My friend actually used the box for a while and found the noise to be an annoyance if the gain structure wasn't exactly ideal, so this would be a great thing to change.
Basically, removing the stock supply and putting it in another box would quiet the Big Knob down immensely. We tried playing with caps around the diode bridge and in other sundry places, but concluded that the hash radiated from the PSU coupled directly into the audio PCB, so little bypasses and the like affected only those 60 Hz harmonics that are completely supersonic, and not even close to "just above 20 kHz".
I put the Big Knob on an APx-555, and the attachment is an FFT of the analyzer residual with a 1.01 kHz +6 dBV tone as input. We used 1.010 kHz rather than something simple like 1 kHz to get the harmonics to not line up with multiples of 60 Hz, so you could see them directly. The graph is truncated to 5.5 kHz, but the harmonics keep going... and going... and going... as you look at higher frequencies. With higher frequency inputs, the distortion spurs became larger than the hum/buzz spurs, so there is definitely room for improvement, regardless of the atrocious hum.
You could play with metal screening between the PSU and the audio PCB, but get it wrong and you burn the house down. Again, the easiest plan was to move the PSU into an outboard box, but neither of us wanted to deal with that hassle, so we ignored it altogether.
I'm sure there are a bunch of chip swaps that could help, but the device is extremely cost reduced, so it'd be like an "interior gut" of a nasty house, and then you're stuck with the PCB layout and basic circuit. Maybe not such an awful thing to do, but it didn't seem worth my time or my friend's.
Best of luck!