There is a very similar question to this, but all answers and discussion pertain to just the PC headphones, and not headsets (the headphones with microphones). Gaming headsets have a boom mic and cable with dual connectors (pink/green), both 3.5mm, one stereo (for headphones), the other mono (for the mic). Standard smartphone headsets have a mic on the cable and a single 3.5mm TRRS (tip-ring-ring-sleeve) combo connector. There are plenty cheap ones with active noise reduction, decent audio quality on both headphones and mics, and more importantly, many people already have them. There are also plenty of Bluetooth headsets (with mics).
A possible solution would be building a Bluetooth adaptor that could plug into the intercom, and then pair with the passenger’s headset to allow them to communicate with others. Bluetooth frequencies are well outside the range of any of the nav/com systems, and even so, they would give the pilot a good excuse to avoid passenger distractions during departure /approach (by turning the Bluetooth transceivers off). Resourceful home builders could easily get the necessary electronics for the Bluetooth transceiver (and adjust the impedance as needed).
If the mic (and headphone) impedances are reasonably close, wouldn’t a simple cable adapter be all that’s needed to enable connection?