Is there such a thing as a LAN splitter?

Yes, it's called a hub.  A more modern version of a hub is referred to as a switch.  Most home WiFi routers have a built-in switch with at least 4 ports on it.

An Ethernet switch.

Connect one port to any port on your router, and use the others for whatever PCs or devices you want.

You can get them with anything from a little unit with five ports to up to modular systems with hundreds of ports.

(Note the "switch" name comes from them working like a telephone exchange switching system; it's not a thing that you manually select ports, they all work at the same time).