Brian,
Since no one else has answered, let me share an opinion of what you'll need to do. Every tag needs to be within 700 *feet* of a tag manager. That distance is under ideal conditions (no house walls or other solid objects between the tag and the tag manager) and your mileage will vary. To be a bit conservative, you should probably plan on each tag being within about 500 feet of a tag manager.
However you are permitted to use multiple tag managers on the same account and so long as each tag is within maybe 500 feet of one of your tag managers you should be able to communicate with each tag. Each tag manager must be connected to the internet.
Tag managers do not connect to or communicate with each other. Each Tag manager must connect via Ethernet to a your network router, possibly through a network switch, if your setup needs extra Ethernet ports.
Cheers, Fred