Power comparison is a common theme. For example, when Goku crosses into the Marvel universe, fans often like to see how his Saiyan powers stack up against the likes of Thor or Hulk. Another theme is culture clash. When Goku enters a different fictional world like the world of Bleach, his Saiyan values and the way of life in Soul Society are very different, and this contrast is explored in the fanfiction.
Goku being born with SSJ4 in fanfic would likely make him a force to be reckoned with from infancy. This could result in quicker power-ups, different battles, and maybe even a shift in the balance of power among the characters.
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.
One possible plot could be Goku from the SSJ4 form crossing over into the world of Dragon Ball GT. He could encounter new threats that require his ultimate form to defeat. Maybe he teams up with the other Z - fighters in that universe to face off against a powerful and ancient evil that was sealed away long ago and has now been unleashed.
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.
The plot might involve Goku SSJ4 teaming up with some unexpected allies in the Tournament of Power. He could be using his SSJ4 powers in creative ways, like combining them with the techniques of his new allies to gain an edge over the other universes' competitors.
One possible storyline could be that Naruto is somehow transported to Goku Black's universe. There, he has to face Goku Black who sees him as an intruder. Naruto would have to quickly learn about Goku Black's powers and find a way to fight back using his ninja skills. Another storyline could be that a powerful villain creates a rift between their two universes and pits them against each other. They start off as enemies but then realize they are being manipulated and team up to fight the real villain.
There could be a storyline where Beerus, out of boredom, decides to train Goku Black instead of fighting him. But Goku Black misinterprets this as a sign of weakness and attacks Beerus. This could lead to a battle where Beerus has to hold back at first to avoid killing Goku Black, but as the fight progresses, he realizes he has to use his full power to subdue him.
One popular mui goku crossover fanfiction is 'Goku in the My Hero Academia World'. It's really interesting as it shows Goku trying to adapt to the quirks - based society. Another one could be 'Goku Meets the Avengers'. Here, Goku's raw power clashes with the high - tech and superpowered heroes of the Avengers, creating some really exciting fight scenes.
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.