If you have multiple computers on a network can braina communicate with each other over a home or work network?
No, currently Braina cannot do this but you can use your smartphone or tablet to connect with Braina over WiFi network.
https://play.google.com/store/apps/details?id=com.brainasoft.braina
https://itunes.apple.com/app/braina-voice-control-pc/id1340996795