Percy is the central figure in 'Percy Travels the World Fanfiction'. Alongside him, if the fanfiction stays true to the original series, characters like Tyson could show up. Tyson, being a cyclops, could offer his strength in dangerous situations. And we can't forget about Chiron. He might be guiding Percy from afar, giving him advice through some magical means. There could also be characters unique to the fanfiction, perhaps a powerful witch in a European forest who becomes an ally or an adversary to Percy.
Well, in this fanfiction, Percy might encounter different mythical creatures in various parts of the world. For example, he could meet a yeti in the Himalayas. Or perhaps he stumbles upon a mermaid colony while sailing in the South Pacific. There could also be some ancient magic hidden in the ruins of Machu Picchu that he has to deal with.
In this fanfiction, Percy might have adventures like battling mythical creatures in the Amazon rainforest. He could encounter new demigods and form alliances to face powerful foes.
He could meet his future self. This encounter might be full of surprises as his future self could have different views and experiences. His future self might be more jaded or more powerful.
One possible plot could be that Percy discovers a magical device that sends him to the future. There, he might find a world that has been drastically changed by the actions of the gods in his time. Maybe the demigod camps have evolved into something completely different, and he has to adapt to new rules and powers.
There could be a sidekick character, like a little alien creature named Zee. Zee might be small but is really smart and helps Percy out of many tricky situations during their travels.
Annabeth could definitely be one of his allies. She's smart and resourceful, and her knowledge of architecture and strategy would be useful no matter where in the universe they are. She could help Percy figure out the layout of strange alien cities or fortresses.
Well, in some of the adventures, Percy might encounter strange alien species. For example, he could meet a race of telepathic beings who communicate through colors. He has to learn their unique language to get help on his journey through the universe.
One common theme is redemption. Percy often goes back in time to correct past mistakes, either his own or those of others, seeking a kind of redemption. For example, in some stories, he tries to save characters who died in the original timeline. Another theme is self - discovery. When he's in a different time, Percy learns more about himself and his powers. He might discover new abilities or a different side of his personality.