How can I combine USB-C peripherals into a single cord?
You may be searching under the wrong names. I've (personally) not seen any USB-C hubs. Don't know if a "splitter" is even possible. However USB-C is now commonly used as a "dock" connector.

It run at speeds that allow you to connect monitors, video cards and other high bandwidth devices. If you do a Google search for "USB-C dock" you will find a number of devices that have multiple ports on it including (often) multiple USB-C ports.

With a USB-C dock you only need one plug when you connect up at home, everything else is plugged into the dock.