Can an emulsion be emulsified?
Yes, they're called multiple emulsions (and more specifically: double, triple emulsions, etc.). Usually they're made from alternating polarity phases—water inside oil inside water, for example. There are bulk ways of making them though there isn't great control over how many droplets end up in each encompassing droplet without using microfluidic techniques. David Weitz's lab at Harvard has some interesting work in building microfluidic devices to make multiple emulsions.

I don't know if there are any common natural occurrences but the pharmaceutical and cosmetics industries seem to be the the main parties interested in this stuff as they can be used for encapsulating drugs for time release and the like.