Perhaps Goku arrives in Remnant without his powers initially. He has to learn how to use Dust and the unique combat styles of RWBY world to regain his strength. In the process, he trains Ruby and the others in his martial arts, and they all combine their skills to face an ancient evil that was sealed away long ago but is now awakening.
One idea could be that Goku accidentally travels to the RWBY universe during a sparring session that goes wrong with Whis. He could be mistaken for a powerful Grimm at first, causing chaos. Then, he teams up with Team RWBY to fight a new super - strong Grimm that threatens all of Remnant.
One idea could be that the RWBY characters are transported into the Overwatch universe and have to team up with the Overwatch heroes to fight a new common enemy, like a powerful omnic - Grimm hybrid. Another could be a friendly competition between the two groups in a series of combat trials to see who is more skilled.
In some versions, the female Goku could be part of a prophecy. The two Gokus meet, and at first, there is some confusion and misunderstanding. But as they get to know each other, they discover that they are key to fulfilling the prophecy. They combine their powers and defeat an ancient evil that was threatening both of their worlds.
One idea could be that the RWBY characters are transported to an alternate universe where they have to team up with Rooster Teeth's other original characters to fight a common enemy. Maybe a new type of Grimm that has some connection to a technology that Rooster Teeth characters are familiar with.
Maybe Gine meets Goku during a time when he is facing a great internal struggle. She offers him the motherly love and guidance he never had growing up. This could lead to Goku having a new sense of purpose and inner peace, which in turn affects his relationships with his friends and family on Earth.
Maybe in the fanfiction, Goku helps Videl discover a new power within herself. He trains her in his special way, and she becomes much stronger as a result. It could also involve some comical moments where Goku's naivete about normal life clashes with Videl's more down - to - earth personality.
One idea could be a crossover where Goku somehow ends up in the RWBY universe. He could train the RWBY characters, sharing his martial arts knowledge and helping them improve their combat skills. For example, he could teach Ruby how to better control her speed and use her scythe more effectively in combat.
One idea could be the different combat styles of RWBY and STRQ teams clashing and then learning from each other. For example, Ruby's speed might be something the older STRQ members could be impressed by and give her some pointers based on their more experienced fighting. Another plot idea could be exploring the relationships between the characters from both groups. Maybe Weiss could form a bond with one of the STRQ members over their shared love for music, if that's part of their backstory. It could also involve a common enemy that forces them to work together and in the process, they discover secrets about their respective teams.
A possible plot is that Android 21 has a unique ability that Goku needs to defeat a powerful, upcoming enemy. So he seeks her out and tries to convince her to help. Along the way, they face challenges like other androids who are still loyal to the old ways. Another idea is that Android 21 creates a clone of Goku by mistake while trying to study his power. This clone has some of Goku's power but also some of Android 21's android - like features. They then have to deal with the chaos that the clone causes.
One idea could be that Goku arrives in the Pokemon world by some sort of interdimensional rift. He might be confused at first but then start to explore the concept of Pokemon battles. He could use his martial arts skills to train Pokemon in a unique way, like teaching them special combat moves. For example, he could train a Pikachu to use a move similar to his Kamehameha, but in a more Pokemon - friendly version, like an electric blast with a similar charging motion.
One interesting idea could be the clash of their different power systems. Goku has his ki-based attacks and Super Saiyan forms, while Sonic has his speed and Chaos Emerald powers. Maybe they could have a friendly sparring match to test each other's abilities.