There are 4 floors - base, 1st, 2nd, and 3rd. Each floor has a light fixture. The previous owners used a timer to control all the lights. To save energy my friend decided to install two 3-way light switches at each end (base and 3rd floor) and two 4-way light switches on the middle floors (1st and 2nd). This is an old building so all wires are colored black and each floor also has pre-existing wiring for the light switches but was sealed with a wall plate. We opened the wall plate and tried to identify the wires on each floor using a non- contact volt meter and wired the light switches but here's the problem.
The light switches work on each floor meaning it will either turn some lights on and some off but when you switch any switch, lights for the base, 1st and 3rd floors will turn on and the 2nd floor light is off. When you flip any switch again only 2nd floor light will turn on and the others lights are off. So the lights keep working in opposite directions. We shut the circuit breaker off and on and tried to turn on the lights from 2nd floor and all lights turned on and off fine for one time. But when tried to turn on the light on another floor, only the base, 1st, and 3rd floors work and 2nd floor is off. When you flip the switch again, 2nd floor light is turn on and the others off.
Does anybody know how to fix this wiring issue? Thanks