If I'm understanding you correctly, you need a story that can be readily perceived at three separate levels simultaneously. First --as in Amadeus' excellent answer --it needs to work as its own, stand-alone, compelling narrative. Second, it needs to represent something different --for example, the 2016 presidential election season. Finally, it needs to represent something else yet again, for instance the psychological journey from childhood to adulthood.
It's difficult to think of any actual examples of this. Perhaps the Platonic dialogues, or the parables of Jesus. Maybe some of Kierkegaard's writing, or the stories of Chuang Tzu. In terms of full length novels, the only book that comes to mind is Lewis Carroll's Sylvie and Bruno (but that's more a case of taking three separate narratives and just mashing them together). Samuel Delany's Dhalgren might also be doing something like this, but if so, the underlying allegories are not clear. The same goes for Murakami's work. That suggests you'd be breaking your own new ground in doing this.
Personally, I'm attracted to this type of writing experiment, but in my own experience, the storytelling has always suffered from having to carry the weight of too much symbolism. If you're determined to do this, my advice would be to do as I hinted at above, and make the two allegories very different kinds --not both about historical incidents, for instance, but one of them being more literal, and the other more psychological.