Maybe Muu is a long - lost member of a powerful clan that has some special connection to Naruto's Uzumaki heritage. So he takes it upon himself to train Naruto to help him reach his full potential and also to preserve some ancient techniques or secrets related to their clans.
Well, perhaps Naruto could learn some unique and powerful jutsu from Muu. Maybe Muu has a special training method that focuses on Naruto's chakra control and helps him unlock new levels of power. For example, Muu might teach Naruto how to better utilize nature chakra in a different way compared to what he learned from Jiraiya.
Obviously Naruto would be one of the main characters. And the descendant of Muu would be the other. There could also be other supporting characters like Naruto's friends, like Sasuke or Sakura.
Well, it could be about a character who is a descendant of Muu having some sort of special powers that Naruto discovers. Maybe they team up to fight a new threat in the ninja world.
I'm not sure who the specific author of that fanfiction is. There are so many fanfiction writers out there that it's difficult to determine without more research.
Maybe Kakashi could be the one. He's always been Naruto's mentor in many ways. He has the knowledge and skills to train Naruto for such an unusual task. He could use his Sharingan to analyze the fanfiction and teach Naruto how to spot the dangerous elements within it.
It could be a rogue ninja from a forgotten clan. This ninja might have a vendetta against Naruto's village and has powers that are difficult to counter. So, Naruto has to train to kill him to protect everyone.
The Akatsuki could still be the main antagonists. Since Naruto is being trained by Shisui, they would see Naruto as an even greater threat. His new skills under Shisui's training could put their plans at risk. For example, if Naruto becomes better at stealth and infiltration, he could disrupt their operations more effectively.
There could be internal antagonists within Naruto's own village. Some of the more conservative ninja in the village might not trust Naruto's new - found skills and powers obtained from Zetsu. They could try to undermine Naruto or even attempt to exile him, fearing that he has been corrupted by Zetsu's teachings.
Another option could be Itachi. Although Itachi is from a different village and has his own complex situation, in a fanfiction scenario, he could secretly train Naruto. Itachi has extremely powerful jutsus and a deep understanding of the Sharingan. Training under him would give Naruto a very different perspective on power and combat, not to mention some insights into the Uchiha clan.
A likely main summon could be Gamabunta. He's big, powerful, and has a long - standing relationship with Naruto. He could teach Naruto some really advanced water - based jutsu.