Another potential rival could be a young, prodigious martial artist from a new school of martial arts on Earth. This character could be jealous of Goku Jr's fame and constantly try to outdo him in battles and in the eyes of the public. He might use unorthodox techniques that Goku Jr has to quickly figure out how to counter.
To develop Goku Jr's character further, he could be given more complex emotions. For example, showing his fear in the face of truly overwhelming enemies, rather than always being fearless like Goku. This would make him more relatable. Also, exploring his relationships in more depth, like his friendship with Pan. Maybe they have a falling out over different views on how to protect their world, which forces Goku Jr. to grow and understand different perspectives.
One idea could be Goku Jr facing a new, powerful enemy that has a unique power related to time manipulation. This would force him to train in ways he never has before and seek help from unexpected allies, like some of the older, wiser characters from the original Dragon Ball Z series.
Well, it could be about Goku Jr learning some of Goku's most powerful moves. Maybe Goku teaches him the Kamehameha. They might also go on an adventure together, like fighting a new and powerful enemy that neither could face alone.
In this fanfiction, they might have an epic sparring session. Goku could pass on some of his old fighting techniques to Goku Jr.
Obviously, Goku and Goku Jr are the main characters.
Maybe an old enemy of Goku's who has somehow managed to return. This enemy has heard about Goku Jr and figures that by attacking him, he can get revenge on Goku. This could be someone like Frieza who has found a new way to be resurrected and is more powerful than ever.
A plot idea could be that Goku Jr. discovers a mysterious artifact that has a connection to the Dragon Balls. As he tries to figure out its purpose, he gets caught up in a race against an evil group who also wants the artifact for their own malicious plans. This could lead to him making new allies and having to use his wits as well as his strength. He might also have to face some personal challenges, like doubting his own worthiness to be a hero, similar to how Goku in the original series sometimes had self - doubts.
In this fanfiction scenario, Goku meeting Gine could be really interesting. Gine is Goku's mother, and in a fan - made story, their meeting might involve Gine finally seeing how strong her son has become. Maybe she'd be proud of all his achievements in protecting the Earth and the universe. It could also be a very emotional encounter as Goku has grown up without her presence for most of his life.
A fanfiction might explore the idea of Bardock seeing Goku's life through a time - space rift. He witnesses all of Goku's battles and the friends he makes. Bardock is filled with pride but also realizes that Goku has a different path than the traditional Saiyan way. This makes him question the Saiyan culture he once knew. Meanwhile, Goku starts to have strange dreams about his father, which leads him to search for more about his Saiyan heritage.
In this fanfiction, they might have an epic sparring session. Adult Goku could teach Kid Goku some new techniques, like the Instant Transmission. It would be amazing to see how Kid Goku reacts to Goku's Super Saiyan forms.