I have the coupling in operation for stereo signal: 3-pole, L + R + GND (common ground).

I can't tell from the outside whether it also supports a fourth pole for an additional signal. However, it is sold as a stereo coupling (i.e. 3-pin) and there is only the three-pin variant for stereo signal on the manufacturer's website: https://www.inline-info.com/de....
It's probably best to enquire there via chat.

This coupling transmits the stereo signal, i.e. the left and right channels are transmitted without any problems.