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Servers with more slots available doesn't make it easy for the extra slots to get filled up. See "Joining More Than 4 or 8 Players in a Game" to get started on filling those slots.

If you require more people join your games than is officially supported, (e.g., campaign with 10 players, a versus with 20) follow the steps here.

1. SteamCMD (optional, but recommended route)
   
2. SourceMod (required)[wiki.alliedmods.net]
   
3. SourceMod ABM Plugin (required)[forums.alliedmods.net]

The optional SteamCMD is the official dedicated server for Left 4 Dead 2. It's purpose is to stay running and does not depend on a player to locally host a game. Leaving in the middle of a game will not shut down the server. You can skip this and speed up this guide but it's highly recommended you go this route (at some point).

The secret sauce to all the great servers out there is SourceMod. Although it has "Mod" in the name, it does not mod any game in any way but will crack open the flood gates to some incredible server side modifications. It's simple and easy to install and a go to power tool for serious administrators (even if you're just having fun without mods).

I am the author of ABM and it enables more players to spawn into the game. Admins have quite a bit of power with it (please be responsible). You need the plugin and gamedata file (abm.smx and abm.txt) from the link listed above and in case you missed it on the last link, the ABM README[gitlab.com] will walk you through installing ABM.

I've decided to leave out any gory deets because everything you need to know is well documented at the links provided. If you follow the order above and have just a little patience, you'll be up and running in no time.

Have fun :)