Okay readers, I am not going to spoon feed you a paper this time. In theses #11, #13, and #14, I investigated of the possible relationships among Toole and Waugh and Proust. But I gave so many details, that I virtually wrote an article for you, or at least a paper of a length suitable for the journal Notes on Contemporary Literature, if not longer. So I will truly try to give the idea without giving many details.
In the Toole Papers, the bibliography of Toole's library included both James Joyce's Ulysses and Finnegan's Wake. Toole also wrestled with Catholicism, gentile poverty, and Irish ancestry. My "Dialectic" paper argues that Toole built a complex symbolic connection between Ignatius Reilly and the Medieval and Renaissance ideas about the planetary god Saturn. As I have argued in Evidence of Influences version 2.0, 30n16, and in the "Dialectic" paper, one can study Confederacy's use of Carnival using the framework of Saturnalia from Frazer's Golden Bough.
Critics have discussed at length the connection between Joyce and Frazer. For example, Vickery devotes five whole chapters of his book on The Literary Impact of the Golden Bough to James Joyce, more than for any other writer. (Admittedly, Vickers wrote after Toole, so Toole could not have been influenced by Vickers himself.) Both in general symbolism and the Frazer connection, Toole seems to be more in the literary school of T.S. Eliot and James Joyce than in the literary tradition of such writers as Toole's contemporaries such as Thomas Pynchon.
Thesis: Explore the possible connections and influences of Joyce on Toole's work. If you are ambitious, compare Joyce's Aristotelianism to Toole's dialectic between Neoplatonism and Pragmatic Humanism.