I think you can't as they are hardware encoded.
True. Even if you add something to the INI you won't be able to add it to the weather list in Construction Set and all the other stuff (effects for example).
You can however sacrifice one of the weathers, by changing the sky texture, and edit it's behaviour by attaching scripts to when that particular weather is active for some effects of your own. Not the best option, but the only one that comes to mind if you really need an unique weather type.