The potentiometer adjusts the depth of microphone positive feedback, which changes the amount of bass boost. If it's adjusted too high, the system starts to self-oscillate. Back off a little bit till the oscillation is extinguished, and that is the setting for maximum possible bass boost.
Not any microphone will do. The microphone should have very flat frequency response in bass range of interest, and perfect phase response as well. The microphone must also be able to handle high sound loudness, in my case it was 147 db (470 Pa of sound pressure, RMS). First I hacked a standard microphone to reduce its sensitivity and extend frequency response. It is tricky. Later I found out some piezoelectric buzzers do the job.
The enclosure must be well sealed. I'm not sure what will happen if it has passive subwoofer or a bass-reflex port. My system had a passive subwoofer originally, I have removed it.
The results are not exactly what I wanted, but it does give a good amount of pleasant deep bass. See frequency response change in project logs.