The idea of the Double, or Doppelganger, is well-trod in the world's literature. For example, Dostoyevsky’s novel The Double describes the psychological trauma of Yakov Petrovich Golyadkin, who believes he sees someone who looks exactly like him. Then there is Robert Louis Stevenson's Dr. Jekyll and Mr. Hyde, the tale of one man with two divergent personalities. Vladimir Nabokov’s Despair is narrated by Hermann Karlovich, who falsely thinks another character looks like him, but that character doesn't really and is a false Double. Jorge Luis Borges’ short story, "The Other," has Borges meeting a younger version of himself.
The Double usually works against the person he mirrors; I'll call that person the Single. So the Double has come to be seen as an evil entity. I'm not really convinced anyone has really seen his own Double, so this entire concept thrives in the world of literature and the arts in general rather than in real life. However, we can think of all people as Doubles, since "all men were created in the image of God." So we are all Doubles of God, but falling far short of His own nature and often working against His own ideals.
No doubt there are many more variations a writer could play on this theme, but it led me to wonder why stop with just a Double? And it led me to conceive of a new literary device never before considered in all of the world’s literature: the Triple.
I envision the Triple as something close to the opposite of the Double (I delineate his attributes here as much as I can for the edification of future fictioneers--myself included). The Double, in the final analysis, is an enemy of the Single. The Triple, conversely, is a friend, and serves to thwart the Double. He assists the Single. However, the Triple can’t be “called upon” or conjured up whenever one wants. I see him as somehow at a distance and the Single has difficulty getting near him--almost as if the Triple exists on a semi-spiritual plane. He is always traveling on the edge of the horizon, making his presence known but remaining beyond any grasp, forever protecting himself by maintaining his safe distance. But even so, the Single can sense his true nature, which is to assist him in his battle against his Double. Both the Double and the Triple physically resemble the Single, and the only way to tell them apart is the fact that the Double usually has some kind of expression on his face or says things that only a scoundrel would say or do. The Triple comports himself in a much more gentlemanly way, and serves as a balancing force for the Single, who becomes imbalanced by the actions of the Double.
But if there can be a Double or a Triple, then it follows that the mirroring can be infinite: a Quadruple, a Quintuple, etc. Each nothing more than the reflection, the shard, of someone else's personality. To stop at the Double seems to ignore a potential army of reflections that possess some definable attribute of the Single.
I think there must be a few good novels on this theme.