A plot could be where Naruto and Shikamaru are on a mission and they come across a mute shinobi who has a different fighting style. The mute shinobi is being hunted by an evil group. Naruto is eager to protect the mute shinobi and Shikamaru figures out the motives of the evil group. As they work together, the mute shinobi reveals secrets about a long - lost jutsu that could change the ninja world.
Perhaps in the fanfiction, there's a curse that makes people mute in a certain area. Naruto, being the hero, wants to break the curse. Shikamaru comes up with a strategic plan. They meet a young boy who is also mute like Shikamaru was when he was young in terms of being reserved. The story could revolve around how they all grow and fight against the source of the curse.
One idea could be that Naruto discovers a mute girl in a hidden village during one of his travels. Shikamaru gets involved as Naruto tries to find a way to communicate with her. Maybe she has a unique power that only she can use, but because she's mute, she has trouble expressing it. Naruto's determination and Shikamaru's intelligence work together to help her out.