Perhaps Naruto, as Orochimaru's apprentice, discovers some secrets about Orochimaru's past that make him more sympathetic towards him. This could lead to Naruto trying to redeem Orochimaru in some way. He might use his own positive influence to change Orochimaru's ways, which would be a major shift in the dynamic between them.
One possible plot development could be Naruto struggling with Orochimaru's dark teachings while still holding onto his own sense of justice. Maybe he tries to find a way to use Orochimaru's knowledge for good. For example, he could learn some unique jutsu from Orochimaru and then modify them to be less harmful or more in line with Konoha's values.
One possible plot development could be Naruto's struggle to break free from Orochimaru's control. He might have to face his inner demons and find new sources of power within himself. Another could be his friends trying to rescue him and having to fight against Orochimaru's minions. Maybe Naruto under Orochimaru's control is used to target the Hidden Leaf Village, creating a huge conflict.
One possible plot development could be Naruto learning some of Orochimaru's unique jutsu. For example, he might pick up on Orochimaru's snake - related techniques. This could give Naruto an edge in combat against opponents who are not familiar with such unorthodox attacks. Also, Orochimaru's knowledge of forbidden jutsu might be passed on to Naruto in a modified, less dangerous way, which could then be used to surprise his enemies in future battles.
A character like Sasuke could be further developed in Orochimaru's lab fanfiction. He might struggle more with the dark knowledge he gains there and eventually find a way to use it for the greater good. Another character could be a new, made - up test subject who starts out as a scared victim but then becomes a strong fighter after enduring the experiments. And Kabuto, who is already associated with the lab, could have a change of heart and try to atone for his actions in the lab.
Well, Naruto might discover some new Orochimaru's plan during the rescue. Maybe Orochimaru was trying to use Hinata to get some information about the Byakugan. After saving Hinata, Naruto could go on a mission to stop Orochimaru from achieving this goal with the help of his friends like Sasuke and Sakura.
One possibility is that Naruto's friends launch a rescue mission. They would use their unique skills, like Sasuke's Sharingan or Sakura's medical ninjutsu combined with her combat skills, to find and save Naruto.
One possible plot development could be that they initially fight against each other as enemies, not knowing their relation. Then, through some kind of accident or revelation, they find out they are brothers. This could lead to a lot of internal conflict for both of them, especially for Deidara who has been on the 'wrong side' in the eyes of Konoha. Another development could be that there is a third party who knows about their relation and tries to use it for their own gain, forcing Naruto and Deidara to work together to overcome this threat.
Naruto would likely become more secretive. Since Orochimaru is a very private and often devious character, Naruto might pick up some of those traits. He would probably keep things from his friends more often.
If Naruto were Samui's brother in fanfiction, it would likely lead to some interesting character interactions. For instance, Naruto might have a closer bond with the Cloud ninjas. He could also get involved in resolving internal issues within the Cloud Village. Maybe he would be more welcomed in the Cloud Village than in the original story. Additionally, it could affect his relationship with Sasuke, as he might have a new support system in the form of Samui and her comrades.
In this type of fanfiction, it might also be that Naruto joins Orochimaru to spy on him. The Hidden Leaf Village realizes they need to know Orochimaru's plans from the inside. Naruto, being the brave and somewhat reckless one, volunteers for the mission. He endures Orochimaru's experiments and teachings while secretly sending information back to the village. Eventually, when the time is right, he betrays Orochimaru and uses the knowledge he gained against him.
They would develop in terms of their skills. Under Orochimaru, they would gain a lot of knowledge about chakra manipulation and forbidden jutsu. But with Naruto, they would learn about the power of bonds and friendship. This combination could lead to the development of new jutsu that combines both physical power and the strength of relationships. Also, they would grow in their understanding of right and wrong, as Naruto's moral compass would constantly be in conflict with Orochimaru's more amoral stance.