It's possible but probably most easily with some digital magic. The basic element of your system will be a voltage controlled amplifier (VCA).
You would need six of these to control your three stereo channels (or three for mono).
simulate this circuit – Schematic created using CircuitLab
VCA based on AN-6603 application note.
Next you'll have to monitor the pot with a micro and use the signal to give three analog outputs to each of the AGC pairs.
simulate this circuit
The code for the micro would have to generate the pulse-width modulation (PWM) output signals as follows. (Pseudo code assumes analog in goes from 0 to 100%, 100% being fully clockwise.
// Output at CCW Midway CW
PWM1 = (50 - AIN) * 2; // 100 0 -100
if (PWM1 < 0) PWM1 = 0; // 100 0 0
PWM2 = 100 - ABS(AIN - 50) * 2; // 0 100 0
PWM3 = (AIN - 50) * 2; // -100 0 100
if (PWM3 < 0) PWM3 = 0; // 0 0 100
The PWM outputs are passed through low-pass filters to give a smooth DC control voltage to the VCA cells.
I have absolutely no idea how much distortion or noise the VCAs would introduce and I haven't worked out weather the VCA would give the correct logarithmic response to simulate a log-law potentiometer. Any problems with the log-law could be sorted out in the software with a little work.
All analog solution
It's probably possible to create the VCA control signals from the potentiometer using analog electronics only.
simulate this circuit
The potentiometer wiper goes from -5 to +5 V and is (optionally) buffered by OA1.
OA2 and D1 form a basic precision rectifier which will pass any pot signal from mid to +5 end.
0A3 inverts the pot signal and feeds it to the second precision rectifier built around OA4 which will pass any signal from mid to -5 end.
Finally OA5 is an inverting summing amplifer. With the pot at mid position the voltage on the top end of R6 will drive OA5 output to +5 V. If either of the rectifier outputs start to rise OA5 output will fall. This satisfies the requirements for the midway channel.
Now tell us what on earth you are doing!