A plotline could be that a dark magic from the Harry Potter world somehow leaks into the Naruto universe and starts causing chaos. Harry follows it to the Naruto world to stop it and ends up saving Naruto from the effects of this dark magic. For example, the dark magic could be turning Naruto's friends against him, and Harry uses his knowledge of counter - spells to reverse the effect. He also might have to battle some sort of dark - magic - created monster while protecting Naruto.
One possible plotline is that Harry is magically transported to the Naruto world and discovers Naruto is in danger from a new, powerful enemy. Harry then uses his magic to fight alongside Naruto and his friends, saving Naruto in the process.
Maybe in the fanfiction, there is a prophecy in both the Harry Potter and Naruto worlds that only Harry can save Naruto. So Harry embarks on a journey to the Naruto world. Along the way, he has to overcome differences in their two worlds' magic systems and cultures. Once he reaches Naruto, he uses his unique magical abilities, like the Patronus charm which could have an unexpected positive effect in the Naruto world, to save Naruto from a life - threatening situation that Naruto's own powers couldn't handle.
One plotline could be Naruto being a transfer student at Hogwarts. He might struggle to adapt to the magic system while also showing off his ninja skills. Another could be Naruto teaming up with Harry Potter to fight a common enemy that threatens both the ninja world and the wizarding world.
It could be that a powerful sorcerer in the Avengers' world goes rogue and starts using dark magic. The Avengers don't know how to handle magic, so Harry is called in. He has to face this rogue sorcerer, using his own brand of light magic. Along the way, he might have some clashes with the Avengers' way of doing things, but in the end, they all work together and Harry manages to save the day by defeating the rogue sorcerer and restoring peace in the Avengers' world.
A possible plotline could be that Tayuya is captured by an evil organization, and Naruto goes on a solo mission to save her. He uses his stealth skills to infiltrate the enemy base.
Perhaps Artemis gets lost in a strange dimension that is similar to Naruto's world. Naruto discovers her there and has to protect her from the dangerous creatures in that dimension. He uses his skills and knowledge of the area to lead her to safety. Along the way, they might form an unlikely friendship or even more, depending on the nature of the fanfiction.
One possible plotline could be that Harry, through some magical accident, gets transported into Naruto's world. There, he meets Kurama and is immediately in awe of the powerful fox. He then tries to learn from Kurama about power and how to use it in a different way than he's used to in the wizarding world. Another plotline could be that Kurama's spirit somehow enters the Harry Potter universe and Harry is the only one who can sense it. He then has to figure out how to deal with this strange entity while also keeping it a secret from others in Hogwarts.
One possible plotline could be that Voldemort discovers Harry's abuse through his Death Eaters' spying. He decides to save Harry as he wants to turn Harry to his side and believes that by rescuing him, Harry will be more likely to join him. Another could be that Voldemort has a moment of self - reflection and realizes that the way Harry is being treated is wrong, so he steps in.
One possible plotline could be that Amelia Bones discovers a plot against Harry before it's too late. Maybe she uncovers some dark wizard's plan to harm Harry at Hogwarts and uses her position in the Ministry of Magic to protect him. For example, she could assign extra guards to the school or personally investigate any threats.
One possible plotline could be that Voldemort realizes that Harry is the key to some greater power or knowledge that he wants to obtain. So, instead of killing Harry, he saves him from another dark wizard or a dangerous magical creature. Maybe he sees that Harry has a connection to an ancient magic that could help him rule the wizarding world in a more complete way.
In some fanfictions, Naruto could be facing a powerful enemy that he underestimated. Temari steps in and saves him. This event could then trigger a series of events where Naruto starts to study Temari's fighting style to improve his own skills. At the same time, the two of them could get involved in some political intrigue within the ninja villages, as Temari is from Suna and Naruto is from Konoha. Their relationship could be a key factor in the stability between the two villages.
One possible plotline could be that the female Harry Potter, with her new kitsune powers from the Naruto universe, uses them to fight the dark forces in the Harry Potter world in a different way. For example, she might use her kitsune illusions to deceive Voldemort.