The electrical wiring adds additional wiring to the same principles of 3 way switching. 4 way switch wiring.

Leviton 3 Way Light Switch Wiring Diagram H1 Wiring Diagram
3 way 4 way switch wiring. A 4 way switch has two positions. At the light the black hot wire will pass right through going to the first switch. For 4 way switch wiring you will need two 3 way switches one at each end and then as many 4 way switches as you want in between. In the diagrams below the first switch 3 way common terminal connects to line voltage. A 4 way switch is always placed in between two 3 way switches. If you understand how to wire a 3 way switch youll have no issues with a 4 way switch.
3 way switch diagram. At the lights the hot source is spliced to the black wire running between lights it does not connect to the lights. At the light the black hot wire will pass right through going to the first switch. The electrical source is at the first 3 way switch and the hot wire connects to the common there. For more than two switches one or more 4 way switches are added between the 3 way switches. A four switch configuration will have two 3 way switches one on each end and two 4 way switches in the middle.
You can have an indefinite number of 4 way switches in a circuit. Watch the 4 way switch video below and pay attention. Here 3 wire cable runs between l1 and l2 2 wire cable runs from the last light to sw1 and more 3 wire cable runs from sw1 to the 4 way switch and then to sw2. 4 way switches are a convenient way to operate lighting fixtures from three or more locations. In the first position the contacts are connected straight through so that the switch has no effect. The first switch 3 way travelers brass color connect to one pair of the second switch 4 way travelers black or brass color.
To illustrate the 4 way switch wiring switch boxes and fixture boxes are not shown but are obviously required for every application. Fully explained 4 way switch diagrams. As you will see most 4 way switch wiring is placed between the wiring of two 3 way switches therefore a 4way switch is installed with two 3way switches. 2 wire cable runs from the light to the first switch and then 3 wire is run between all the switches. In this basic 4 way light circuit 3 wire cable runs between all the switches and 2 wire cable runs from the last switch to the light. 2 wire cable runs from the light to the first switch and then 3 wire is run between all the switches.
They all must be between the two 3 way switches. For 4 way switch wiring you will need two 3 way switches one at each end and then as many 4 way switches as you want in between. The circuit neutral is spliced at each switch box through to the light fixture using the white wire.