@lmorgan80 said:
If I buy a tuner box with 4 tuners in it (1 more than the number of TVs I have), is that enough for my configuration?
Only you can know if you want to record more than one channel 
If so, how do I get the tuner output to the remote TVs?
Each TV needs a Plex client.
The Plex client requests the stream from the Plex Server.
The Plex Server fetches the stream from the tuner box.
i.e. all data go over your home network, preferably ethernet wire.
I personally don’t recommend to rely on WiFi for “big screen” devices.
