Intermediate switch an intermediate switch is a three way light switch. You would just continue from one 3 way switch box with the 143 three conductor cable two colored traveler wires a white neutral and a bare or green ground wire in and out of each four way switch box.

938c8c Wiring Diagram For 1 Lamp 2 Switches Wiring Library
Intermediate light switch wiring diagram. The four terminals of intermediate switch construction and its operation are shown in fig below where the 4 contact points may be known as a b c d. The source is at sw1 and 2 wire cable runs from there to the fixtures. It is used when you have three or more switches controlling one light the middle switch needs to be an intermediate light. When the switch knob is up the terminal contacts of intermediate switch connect terminal a with terminal c and terminal b with terminal d as shown in fig 1a. See the light switch wiring diagrams above and below. This diagram illustrates wiring for one switch to control 2 or more lights.
In some countries the four way is called an intermediate switch. The hot and neutral terminals on each fixture are spliced with a pigtail to the circuit wires which then continue on to the next light. Intermediate switch wiring diagram new cable colours the intermediate light switch is used where three or more switches control one light and used in conjunction with two two way light switches to achieve this. It is effectively two single gang intermediate switches on one face plate.