You can run multiple Empyrion games on your server using multiple EAH-Tool installations.
1) Each Empyrion Server installation has its ownEAH installation in the EmpyrionAdminHelper folder. You can use these or create your own folders. Important is that each game needs its own EAH tool.
2) Each one needs its own port to communicate. EAH speaks via port to the game. The default port is 12345. With to tools running, this will not work. You have to have a different port for each tool/game. You have to set this port at two locations:
In the Mod: Go to your Empyrion Server installation folder down to Content\Mods\EPM (...\SteamLibrary\steamapps\common\Empyrion - Dedicated Server\Content\Mods\EPM). Here you find a Config.txt. Open it and change the port line from "Port:12345" to whatever port you want to use. For example: "Port:12346". If the folder or file is not existing yet, start EAH and the server ones.
Enter the same port in the according EAH tool (same game installation). Go into the config and change the API Port (see screenshot)
3) Of course you also have to set up each tools path to the game, its dedicated.yaml and dedicated.cmd. You find these infos in the Config on the first page (see screenshot). But they should be set up automatically. Just make sure they are right.
4) Thats all. Now restart the tools and the games and it should work.