It's not a stupid question and the answer is "kind of."
You cannot do it passively. I.e.: Simply split the copper N ways. But you can run a single "backbone" connection to a remote Ethernet switch, and branch out from there.
So, for example: I have my alarm system, an over-the-air TV network tuner and networked DVR all in the same spot in the corner of the basement. It's at the opposite corner as the computer room. I ran a single cable from our computer room to that location, put a 5-port switch there, and plugged them all in.
It's configuration-less, unless you buy a managed switch, then it's optionally configurable so you can examine the status of the switch's ports, etc.. (I like managed switches as they can aid network debugging--and security, if you know what you're about and want to go to the trouble.)
Obviously the placement of that remote network switch will have to be environmentally acceptable for its electronics and you might want to consider a small UPS.
You can also do the backhauling with WiFi. Say a pair of Ubiquiti Nanostation Loco M5's. One's connected to your network, the other to the remote Ethernet switch. But that starts to get iffy if you have a lot of cameras, you're using several 8MP cameras, or the WiFi connection isn't that great, as your bandwidth will be greatly limited over that 5GHz wireless backhaul.
I'm actually eventually going to do that 5GHz backhaul thing with our µBarn, about 100' from the back of the house. Then I'll put a WiFi AP up in the peak on the inside and an IP camera looking out at the yard. Maybe another pointing back at the house. None of this because I need to, but more for the giggles
Thanks for the solution. Normally I wound hire someone to do the job instead of me. But you can't find a lot of technicians around here. Also the 3-4 technicians you can find are very expensive and not well educated.