The Chia protocol is set up in a way that is friendly for having many systems on a local network communicating to a single farmer, through something called a "harvester". You generally do not want multiple full nodes on the same local network to avoid networking conflicts and it is really not required, due to the efficiency of harvesters.

https://github.com/Chia-Network/chia-blockchain/wiki/Network-Architecture
https://github.com/Chia-Network/chia-blockchain/wiki/Farming-on-many-machines