The theme of legacy is quite common. Goku is a legendary figure, and in fanfiction, his legacy - what he leaves behind for future generations - is often explored. Also, the theme of redemption can be found. Maybe Goku made a mistake in the fanfiction's plot, and he has to redeem himself. And the concept of the hero's journey is also there. Goku's path as a hero, with its challenges, growth, and revelations, is a recurring theme in serious Goku fanfiction.
One great serious Goku fanfiction is 'Goku's Redemption'. It delves into Goku's inner struggles after a major battle where he made some tough decisions. Another is 'The Trials of Goku' which focuses on his journey to master a new form while dealing with the politics of the Saiyan race. And 'Goku's Ascent' is also worth reading, where he tries to reach a new level of power to protect his family and the Earth.
Well, Vegeta would be a likely character. He might be initially suspicious of the female Goku. Maybe he thinks she's a threat or just can't believe there's another Goku - like being. He could be there to add some comical moments as he tries to understand the situation.
Another possible main character could be the villain that forces the two Gokus to meet. This villain could be a new, super - powerful threat that the two Gokus need to deal with. Their meeting becomes a crucial part of the story to defeat this powerful foe.
One of the characters who could betray Goku is Piccolo. Although they've been allies for a long time, in fanfiction, things can change. Perhaps an ancient evil force takes control of Piccolo's mind and makes him turn on Goku. Or it could be Krillin. He might be influenced by an outside force that convinces him Goku is becoming too dangerous. Also, don't forget about the Kais. If there's some sort of power imbalance or a threat they perceive from Goku, they might betray him to maintain the order of the universe in the fanfiction.
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.
One interesting fanfiction could be about Goku and Black Goku teaming up against an even greater threat from another universe. In this story, they might initially be at odds but gradually learn to work together, using their unique abilities to save the multiverse.
In fanfiction about Goku and Goku Black, a common concept is the alteration of their power levels. Writers may give Goku new forms or boost Goku Black's abilities in unexpected ways. There can be stories centered around Goku Black's adaptation to the main timeline's culture and society. For example, he might have to deal with the everyday life in addition to his evil plans. And there are fanfictions that focus on the psychological impact of their battles on each other, like how Goku might be affected by constantly facing an evil version of himself.