Well, there are some great ones. A lot of fanfiction in this area explores the power of Goku in his SSJ4 form in the context of the Dragon Ball Super universe. Some stories might focus on battles that Goku could have in this form against new and powerful enemies, while others could be about his relationships with other characters while being in this super - powerful state. It really depends on what you're interested in.
One common theme is power exploration. Writers often explore the full extent of Goku's SSJ4 power in Dragon Ball Super scenarios. Another is the idea of new battles. Fans like to imagine Goku in SSJ4 facing off against different villains. Also, friendship and family themes are common, like how Goku's new power affects his relationships with his friends and family.
Well, in Dragon Ball Super SSJ 4 Goku fanfics, his character development is often quite interesting. His SSJ 4 form is not just about physical power. He could start to understand the spiritual side of his power more deeply. He might go on a journey to find out the true origin of the SSJ 4 form, which leads him to ancient Saiyan or Namekian knowledge. This new knowledge could change his perspective on his role in the universe. He could also develop better leadership skills. Since he's so powerful in SSJ 4, others might look up to him more, and he has to learn to lead in battles and in making decisions that affect the whole group, not just himself.
In Dragon Ball fanfic, Goku SSJ often has super strength, like being able to lift extremely heavy objects with ease. He can also move at incredible speeds, making it hard for enemies to even see him coming. His energy blasts are much more powerful than in his normal form, capable of destroying large structures or powerful foes in one shot.
In some fanfics, a great plot twist is when Goku discovers a new, hidden power within his SSJ 4 form. This power could be related to his Saiyan heritage in a way that no one, not even Vegeta, knew about. Also, there might be a plot twist where the Dragon Balls are used in a completely different way. Instead of just wishing for power or bringing back the dead, they could be used to change the rules of the Saiyan power - up system, which would have a huge impact on Goku's SSJ 4 form.
In some fanfics, Goku SSJ's character development might focus on his relationship with his family. He could become more protective and understanding of his family's needs. For example, he might take more time to train Gohan and teach him important life lessons along with martial arts skills.
One interesting story could be about a new villain who forces Goku to reach the SSJ4 form in a completely different way. Maybe he has to combine his Saiyan powers with some ancient energy source on a new planet. Another could be a fanfiction where Vegeta finally masters the SSJ4 form before Goku and has to face a powerful foe alone.
Goku is almost always a main character. His journey to master or use the SSJ4 form in new and exciting ways is a common theme. Vegeta is also often included, especially when it comes to rivalries and his own pursuit of power in the form of SSJ4. Sometimes, other Saiyans like Trunks or Goten might also be featured, especially if the story involves the next generation of Saiyans and their relationship with the SSJ4 transformation.
In this fanfiction scenario, it could be an extremely emotional encounter. Goku, who has grown so much in Dragon Ball Super, finally meeting his father Bardock. Maybe Bardock gets to see how his son has not only become a powerful Saiyan but also a protector of Earth. It could lead to some interesting exchanges about Saiyan heritage and the future of the Saiyan race.
Caulifla and Goku's relationship in fanfiction could be really interesting. Maybe in this fanfiction, they start as rivals. Caulifla, with her Saiyan pride, wants to prove she's stronger than Goku. But as they fight more, they begin to understand each other's fighting styles and develop a mutual respect. This could lead to some really cool training sessions where they both learn new techniques from one another.