Naruto could be a mediator. Since he comes from a different world with different power systems, he might be able to bridge the gap between the Shinto gods and the demigods in the Percy Jackson world. He could use his understanding of loyalty and friendship from his own story to help resolve conflicts.
He might be a catalyst for change. His presence could disrupt the status quo in the Percy Jackson - Shinto god setting. Maybe his unique chakra system is seen as a threat or a source of power that different factions want to control. So he becomes a central figure in a power struggle that involves the Shinto gods and the demigods, and his actions determine the fate of both worlds in the fanfiction.
He might be an antagonist at first. His different set of powers and his somewhat aloof nature could make the demigods view him as a threat. But as the story progresses, they could discover that he's actually on their side and has his own reasons for his actions. For instance, he could be trying to stop a greater evil that the demigods are not aware of yet.
One way is through a crossover of quests. For example, Percy could be sent on a quest that involves the Shinto gods' realm. Maybe he has to retrieve an important artifact that is sacred to the Shinto gods. This would bring his world of Greek demigods and the Shinto gods' domain together in an exciting adventure.
A possible plot could be that Percy is summoned to Japan by the Shinto gods to help stop an ancient evil that is threatening both the Greek and Shinto worlds. This evil could be a powerful demon that has the ability to disrupt the balance between the two pantheons.
Well, one way could be that in the fanfiction, Naruto's powers are somehow related to the Shinto gods. Maybe Naruto is on a quest in the Percy Jackson universe and he encounters a Shinto god who bestows him with a new power or task. For example, a Shinto god could give Naruto the ability to control water in a more magical way, similar to how demigods in Percy Jackson have special powers related to the gods.
He could be a mentor figure. Goku has a lot of experience in fighting powerful enemies and growing stronger. He could teach the demigods in Percy Jackson's world some new combat techniques.
The unique combination of different mythologies. Percy Jackson is based on Greek mythology, and when you add Shinto elements, it creates a whole new and exciting world. For instance, the idea of demigods from Greek mythology interacting with Shinto kami is really cool.
She often plays the role of a protector. Hestia's connection to the hearth gives her a sense of guardianship. In fanfiction, she might protect the demigods from the more malevolent forces. For example, she could keep them warm during a cold and dangerous night on a quest.
Excalibur could play the role of a unifying force. In fanfiction, it might be the one thing that different groups of demigods or even gods are after. Its presence could create alliances and rivalries. Say, the campers at Camp Half - Blood and the Roman demigods from Camp Jupiter might have to work together or fight over Excalibur. It could also be a symbol of a greater power that is emerging in the Percy Jackson world, leading to new prophecies and quests.
She often plays the role of a love instigator. She can create romantic tension between characters, like making two demigods who initially dislike each other start to have feelings. This adds an interesting dynamic to the fanfiction story.
Maybe Percy unknowingly breaks some ancient and very strict laws of the Gods. For example, he might interfere with some sacred rituals or places that are off - limits to mortals, even demigods like him. In the fanfiction world, the Gods could be very unforgiving when it comes to such violations and decide to kill him as a result.