Fanfiction can enhance understanding in multiple ways. Firstly, it can provide additional backstories for the characters. Maybe we learn more about Annabeth's family history or Percy's early days at camp. Secondly, it can explore the cultural aspects of the PJO world more thoroughly. The Mark of Athena fanfiction might include more details about the Roman and Greek cultures that are so important in the series. This helps the reader to better understand the context and the significance of various elements in the PJO universe.
It can enhance understanding by showing different takes on the existing story. For example, a fanfiction might explain a certain event from a different character's point of view, which can give new insights. It can also expand on the lore. If there were some parts of the mythology in the series that were a bit unclear, fanfiction might clarify them.
Reading The Mark of Athena fanfiction allows you to see how other fans perceive the characters. You might notice new character traits or relationships that you hadn't thought of before. Fanfictions often explore the consequences of actions more deeply. So, if something happened in the original book, the fanfiction might show how it affected the characters in the long run and in different situations, thus enriching your understanding of the PJO world.