You would probably just proceed from a single three-way switch box Along with the fourteen/three 3 conductor cable (Two colored traveler wires, a white neutral, plus a bare or eco-friendly floor wire) out and in of each 4-way switch box. The white wires get spliced by in Each individual switch https://3-wayswitchwiringdiagram24668.rimmablog.com/14892968/the-definitive-guide-to-wiring-diagram-for-3-way-switch