How close are the switches to one another? Another option for multiple point dimming is to use Lutron Caseta dimmer at the power-in point and then you can use remote Pico switches in all other locations, even where there is no wiring for the circuit.
The Pico remote saved me from doing a whole lot of destructive rewiring when a customer did not explain that they wanted to control a set of kitchen lights from the entrance and the kitchen until after the sheetrock, cabinets and countertops were in. I just put a Caseta in at the switch in the kitchen and then put a Pico remote at the entrance.
Yes, the Pico remotes run on li-ion coin batteries, but are guaranteed by Lutron for 10 years of use, and I added a nice, small note in the panel which reminded the customer that the switch at the entrance was battery controlled and the battery may need replacement in approx. 10 years.
Another option is to use a Lutron master dimmer switch at the point where power enters the 4 way lighting circuit and then use slave dimmers at the other 2 locations.
Another option, as others have suggested, is to put a 3-way general purpose dimmer at the point where power enters the lighting circuit, a 4-way general purpose dimmer at the center point of switch circuit and a 3-way general purpose dimmer at the point where the switch leg enters the lighting circuit.
Just my two cents.