To answer your question I would continue the list of themes and topics from the previous post, and then see where there are connections to novels and a plays you have already read. Some additional themes to consider:
2. bullying/ good vs. evil
4. social class distinction -- effect on relationship
5. America as a land of (new) opportunity
6. mental/physical survival of a crisis
7. suicide/attempted suicide
The list could go on, but the next step is to look for those elements in other novels. Just having the theme in common is a start, then you need to determine if the authors are making a similar point. With a little brainstorming, you may discover that what at first seemed like a stretch, actually works for the comparative purposes. For example, The Great Gatsby is about several of the topics listed above -- what can be done with the commonalities?
The Kite Runner shares several similarities with Elie Wiesel's Holocaust memoir Night. Both feature tense father-son relationships, displacement, and narrators who are quite honest about their faults and their sometimes self-centered motives.
In regards to the important role that competitive friendships play in The Kite Runner, John Knowles novel, A Separate Peace, is also a good comparative work. In Peace, the narrator Gene wants to be friends with Finny (his roommate and the most popular boy at Devon School), but he is also jealous of Finny's charm, just as Amir is jealous of the attention that Baba bestows upon Hassan. Likewise, Hassan and Finny are both athletic and easy-going, while Amir and Gene are introverts who doubt their physical prowess. The most significant similarity is that both narrators--Amir and Gene--betray their "best" friends. Gene's betrayal actually leads to Finny's death. But even with those betrayals, the betrayed--Hassan and Finny--demonstrate the remarkable power to forgive.