BrewPi controls a single environment. It doesn't know how to deal with more than one.
But, you can run multiple BrewPi instances, each with its own Arduino controller and own web page, on a single RPi.
I have four BrewPi instances running here, controlling a keezer, two fridges, and a cold-season ferm chamber. Three of the instances communicate wirelessly over Bluetooth, the other is hooked up via USB...
Cheers!
[edit] The 8-channel relay module is a less-than-optimal component in this application, as it means you'll have to have multiple Arduino controllers huddled around the relay module, with AC wires radiating out to all your chambers. You'll also need to provision enough AC input connections to the relay module to handle all those units - you're not going to run four fridges from a single line cord to a wall outlet. Sounds like a nightmare to me...