Notice that this snippet uses a describer, cool, not a classifier. This isn't a coincidence. What happens if we replace cool with a classifier, like Swiss?
He's actually a really Swiss dude.
It sounds a bit strange because officially you can't be more or less Swiss; you either are or aren't.
Having said that, in reality we do sometimes say things like "He is so Swiss" or "This town is very Texas."
When you use a classifier in this way (i.e. with an intensifier) it usually sounds more emphatic, or even comical, because it's not typical usage.
