Note: Family Sharing is not the same thing as iTunes Home Sharing, nor is it the same thing as associating multiple devices e.g. computers with the same single iTunes account.
You are allowed a total of five computers (Mac or PC) to be connected to iTunes Home Sharing, see - Get help with Home Sharing - Apple Support
I believe the limit for Apple TVs is the same i.e. five and also is the same for iOS devices i.e. iPhone + iPad + iPod Touch meaning you could have five computers, five Apple TVs and five iOS devices all connected to the same single computer acting as a Home Sharing server.
A workaround might be to have two (or up to five) computers each logged in and authorised to the same Apple ID and each able to Home Share to five Apple TVs and iOS devices and of course computers running iTunes. This would then give you a hypothetical maximum of 25 computers, 25 Apple TVs and 25 iOS devices. This approach would require having five separate iTunes libraries - one per computer acting as a Home Sharing server. Now that Apple make it possible to auto-download Music, Movies and TV Shows when purchased it is easier to keep them all up to date.