I am 99.9% sure this is not currently possible, but why couldn’t Omniports both send and receive using a splitter of some kind. Correct me if I’m wrong, but I don’t think anything would happen to a momentary Aux switch from a ping from one side of the splitter that sends a message to something (amplifier, pedal, etc.) through the other side of the splitter.
Edit: upon reflection I realized the Aux switch would send the tip or ring or tip/ring to the other side. This is why I buy midi controllers and not design them. 