"Satire" is a very broad word – maybe you could break it down into types, and then taxonomize them – that is, list them in order of their “something.”
I’m thinking of social satire, vs. personality satire vs. moral satire, etc. In your literary pieces, for example, the satire of “Rape of the Lock” is of a different order from “Gulliver’s Travels” in that Pope is satirizing**** while Swift is satirizing *****. (I’m purposely not filling in these blanks; the joy of your assignment will be how you fill them in.) Here are just four ways satires can differ from each other:
1. Subject: Some satires are critical of personal behavior or traits, while others are critical of societal wrongs, injustices, collective values and illusions, etc. Still others criticize those in power or influence. While all satire is critical, the objects of that criticism vary in degrees of personal reference;
2. Tone: A humorous tone is assumed in the term “satire,” but the viciousness of the attack, the anger or seriousness of the satirist, the egregiousness of the wrong (think of The Rape of the Lock’s tone vs. Gulliver’s Travels) all vary and are reflected in the language, the narrative voice, etc;
3.Literary artificiality: Gulliver’s Travels tells its story is a different way from The Rape of the Lock (not just prose vs. verse). They have found two different ways to (in Aristotle’s terms) “imitate an action.”
4.Level of Sophistication: There is such a thing as “classy” vs. “non-classy” in literature, determined in large part by the intended (contemporary with the author) audience.
Anyway, my idea is for you to make an essay out of “the kinds of satire,” making a taxonomy (arranging like items by listing their differences) of them. You could easily incorporate examples from previously studied literature. The secret of a good essay is one that intrigues you while you work.