Well, in fanfiction, it could also be that there is a common enemy. For example, a powerful ancient being that is a threat to both the demigod world of Percy Jackson and the world that Agents of Shield operates in. This would force them to team up. Percy's powers like controlling water could be really useful in some of the situations that Agents of Shield faces, like dealing with underwater threats or putting out fires in a unique way.
Another possibility is that there is a prophecy in the Percy Jackson universe that somehow links to the events in the Agents of Shield world. Prophecies often drive the actions in the Percy Jackson series. So, if there was a prophecy that said something like 'The demigod must join the agents to save both worlds', it would be a great way to bring Percy into the Agents of Shield fanfiction. He would bring his own set of skills, like his combat skills with a sword, which could be very different from the fighting styles in the Agents of Shield world, creating interesting interactions.
One way they could merge is through a magical portal. Imagine if the demigods from Percy Jackson's world accidentally stumble upon a portal that leads them to Westeros. They might bring their unique powers, like Percy's control over water, and it would disrupt the power balance in Game of Thrones. For example, they could help in battles against the White Walkers, using their god - given abilities. This would change the whole course of the Game of Thrones story.
Well, in many fanfics, they merge the universes by having some sort of magical or scientific accident. For example, in one fanfic, a portal opened up between Camp Half - Blood and the Young Justice headquarters. The female Percy Jackson then gets sucked into the Young Justice world and has to adapt.
Another way is when a character from one universe is sent to the other on a quest. Let's say Percy Jackson is sent to the Naruto world to retrieve an object that has somehow ended up there. His presence then starts to mix the two universes as he befriends the ninjas and they learn about his world.
Writers often start by establishing how a fem Percy Jackson could end up in the Harry Potter universe. Maybe through a magical portal or some kind of cross - dimensional spell. Then they find ways to make her demigod powers interact with magic. For example, her ability to control water might have an unexpected effect on a magical water - based spell in Hogwarts.
Well, Percy could use his water powers to help the Agents in a situation where they face a threat related to water, like a flood created by a villain. Maybe he'd be initially mistrusted by the Agents, but then prove his worth.
A possible combination in fanfic could be through a character's backstory. Let's say there's a character who has a hidden mutant gene but was raised in the world of S.H.I.E.L.D. As they grow older, their powers start to manifest. This character could then act as a bridge between the two universes. They could introduce the X - Men to the world of S.H.I.E.L.D. and vice versa. This could lead to all sorts of interesting interactions, like the X - Men learning about S.H.I.E.L.D.'s protocols and the Agents of Shield getting to know more about mutant culture.
One way could be through magic. In the world of Harry Potter, Tom Riddle is a powerful wizard. In Game of Thrones, there is also magic, albeit different. Riddle could perhaps use his dark magic to cross over into the Game of Thrones universe. Maybe he'd be drawn to the power struggles there, similar to his quest for power in the wizarding world.
Well, if we consider the concept of gods in both universes. In Naruto, Kaguya was like a god - like being. In Percy Jackson, there are the Greek gods. There could be a plot where the Greek gods sense Naruto's power as the son of Kaguya and either try to recruit him or see him as a threat. This could lead to all sorts of adventures as Naruto tries to find his place in this new world full of demigods, monsters, and strange magic.
At first, it might be a relationship of mutual suspicion. The Agents of Shield are used to dealing with threats within a certain framework, and Percy with his magic powers and connection to the Greek gods would be something completely new. But as they face common enemies, like a powerful demigod - turned - villain or a group trying to use Greek magic for evil, they would start to trust each other more.
In some fanfictions, the settings are merged. So you might have Camp Half - Blood with a touch of Hamilton - era architecture or the characters from Hamilton having to deal with the monsters from Percy Jackson's world. The values of loyalty and friendship from Percy Jackson can also be contrasted with the power - hungry and ambitious nature of some Hamilton characters, creating really interesting storylines that are more than just the sum of their parts.