How can I remove this thermostatic mixing shower faceplate?

This shower has a temperature selection knob, which operates separately from the water pressure/on-off knob. The selection is unresponsive, water temperature does not rise or fall when the knob is twisted.

I thought I’d start by taking the faceplate off and learning more, possibly replacing a cartridge. But pulling off the faceplate is blocked by the black ridged ring on the knob:

I see no indication of the manufacturer or model of this shower. Any advice for how to proceed? This is what it looks like behind the knob, peeking behind the faceplate when it’s slid out as far as I can:

It seems like I might be able to address the problem there. But with the faceplate on, I can’t access those parts. Other detail in case relevant: this temperature selector knob controls three shower heads, two of which share one on-off knob and the third on a separate on-off.