Do aviation intercoms have a standardized compatibility with radio stacks? I have been seeking an intercom unit for a Cessna 172N that has four seats but only two headset jacks, and I would like my rear passengers to be able to communicate without yelling.

Aviation intercoms have external radio transmit switches, but the airplane also has its own built-in radio transmit system.  How does the transmit function trigger in this type of system?  Do they send a certain audio signal frequency or tone to the COM stack that tells it to transmit?

Are most intercoms universally compatible with all com stacks if they use the same plug types?
This is a good question - the comments above answer most of it, but here are some more details:

Short answer: yes, they are pretty much standardised. Any modern GA intercom will work with any modern GA radio.

Part of the job of the intercom is to tell the radio when to transmit, and to route the correct microphone signal through to it. This is almost always done using a single wire which signals "transmit now", and a pair of wires for the microphone signal from the headset corresponding to the PTT button that was pushed.

On more advanced integrated setups, the signals might be transmitted over a digital bus, but outside of fully integrated setups like the G1000 (and even then on some models), there are always ways to connect standard aircraft radios to the intercom.