When it comes to synonyms for the phrase "study at parody," there are a number of options to choose from. One alternative might be "examine at satire," which suggests a similar focus on analyzing and critiquing humorous or ironic commentary. Another possible phrase could be "research parody," which emphasizes a more academic approach to understanding the genre and its role in cultural discourse. Other options might include "explore humorous commentary," "delve into comedic critique," or simply "analyze parody." Ultimately, the choice of phrasing will depend on the specific context and intended audience, as well as the writer's personal preference.