[radiotechnician]

For old phones with carbon transmitters.

If you want to use the phones as an intercom system, not connected to the Central Exchange, A DC source is required. This source is connected in series with a RET (retardation coil). This system provides transmitter current to each phone. The voice circuit travels via the impedance of the RET.

Then all three phones, and the RET and battery are connected in parallel.

That does not address the signalling issue. Other have suggested a third wire/button/buzzer.

Telco RET units are rather elaborate, and have several windings.
Your RET might be as simple as the coil and core from a 12 volt DC relay, 200 ohms or so.

Each phone will have two wires, Tip and Ring.

The RET system will have one wire of the battery called Tip and one wire of the coil called Ring.
The other ends of the coil and battery are joined together. Join all Tips together, then join all Rings together.

Battery 12 volts or so.

The North American phone system seems to have grown up around four basic coil types:

Induction
Repeating
Retardation
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Attached is end view of a RET coil, and how phone service workers use it.