One possible plot could be that Harry is wrongly accused of a crime in the wizarding world, perhaps something related to dark magic. The police, who might be a new magical law enforcement unit, rescue him from an angry mob. They then help him clear his name by finding the real culprit, who could be a Death Eater in disguise trying to frame Harry to cause chaos in the post - Voldemort era.
The plot could involve the goblins rescuing Harry when he is being wrongly accused of a crime in the wizarding world. They could believe in his innocence and use their unique skills and knowledge of magic to keep him safe. Maybe they help him prove his innocence later on. They might also have their own motives for helping Harry, like they see him as a key to some sort of change in the relationship between wizards and goblins.
Well, it could be that Harry is found by the police in a Muggle area while on the run from some dark wizards. Maybe he's using magic to defend himself and the police are shocked to see it.
In this kind of fanfiction, perhaps Harry is rescued by the Order of the Phoenix earlier than in the original story. They might have realized the Dursleys' mistreatment sooner. Then Harry could start his magical training earlier, away from the hostile environment of the Dursleys' home. He may also form closer bonds with other members of the Order, like Sirius, who could play a more active role in his upbringing.
One possibility could be that Voldemort rescues Harry Potter for some self - serving reason. Maybe he realizes that Harry holds the key to a greater power that he wants to obtain. So, instead of killing Harry, he saves him from another threat, like a powerful dark wizard who is trying to overthrow Voldemort and sees Harry as a useful tool as well. In this fanfiction, Harry would be in a very strange situation, having to trust Voldemort at least temporarily.
The plot could involve a magical artifact that Harry Potter is trying to protect. This artifact has somehow made its way into the world of NCIS. Dark wizards want to get their hands on it and will stop at nothing. Harry is in over his head as he tries to deal with both the Muggle law enforcement and the powerful magic of his enemies. NCIS agents, with their own code of honor and sense of justice, step in to rescue Harry. They start to learn about the magical world as they help him, and together they come up with a plan to keep the artifact safe and get Harry back to Hogwarts.
Maybe Prince William stumbles upon Harry Potter during one of his wizarding battles. Using his royal influence or some hidden magical ability (in this fictional scenario), he manages to save Harry from a dangerous situation, like a Death Eater attack.
Maybe the Fem Harry Potter is being hunted by Voldemort's followers in a new and unexpected way. The NCIS agents rescue her, but then find out that there are spells on her that are affecting the Muggle world around them. They need to find a way to break the spells while also keeping her safe from the Death Eaters. This could lead to some interesting interactions between the two very different worlds.
In this fanfiction, the Delacours might rescue Harry by using their knowledge of the wizarding world outside of Hogwarts. They could have some secret passages or allies that Harry wasn't aware of. For instance, they could lead Harry through a hidden route in the French wizarding community that the enemies don't know about.
In a 'Harry sold rescued Snape' fanfiction, the plot could start with Harry learning that Snape is held captive by a group of dark wizards. Harry realizes that he needs certain magical supplies or potions to break Snape free. Since he doesn't have the funds to buy these items, he decides to sell a rare spell book that he found in the Room of Requirement. This spell book has some unique spells that could potentially be used against the dark wizards. But once he sells it, he discovers that the buyer has some ulterior motives and is somehow connected to the group holding Snape. Now Harry has to not only get the spell book back but also figure out how to use it to rescue Snape while dealing with the new threats that have emerged.
Perhaps there is a prophecy in both universes that foretells of a great danger that only the combined forces of Harry Potter and the Avengers can face. When the Avengers learn of this, they travel to the wizarding world to find Harry. They rescue him from an immediate threat so that they can all prepare to face this greater danger together. The Avengers could introduce new ways of fighting and thinking to Harry, while Harry could share his knowledge of magic with them.