Allowing Civ to use more than 18 players already mods the game, so by definition you can't do that and play modless.
However, I think you mean that you want to just add the possibility to play with more civs, without changing or modding anything else.
That's possible, you'll need to find one of the "50 Civs" dlls that are floating around. I'm not sure where to find them (I play heavily modded games so I wouldn't have a use for it), but they were popular for a while and should still be around somewhere.
If you don't find one for your version of the game, then you could compile one yourself. The change in the source code is extremely easy, but setting up the environment to successfully compile the dll can be tricky. There are good tutorials for that in the modding section though. I used one without prior experience and got the dll compiled within a day.