One idea could be that Mewtwo somehow gets transported to the Harry Potter universe. It could be mistaken for a very powerful magical creature. Harry and his friends could initially be wary of it, but then realize it has no intention of harm and they team up to fight against the dark forces in the wizarding world using Mewtwo's psychic powers.
A more complex plot could involve a prophecy in the wizarding world that mentions a 'creature from another realm' which is Mewtwo. The Order of the Phoenix believes that Mewtwo is the key to defeating Voldemort. So, they try to enlist its help. However, Mewtwo has its own agenda and moral code. Harry has to convince Mewtwo to side with them, which is not easy as Mewtwo is distrustful of humans. This could create a lot of tension and interesting character interactions.
In a'mewtwo meets mewtwo fanfiction', it could start with the two Mewtwos being summoned by an unknown force. At first, they are confused and defensive. As they interact, they find out that their memories of creation and the pain of being experimented on are very similar. They might then decide to search for the source of this unknown force together. Along the way, they face various challenges, like other powerful Pokémon trying to stop them or humans who fear their combined power. But through their shared experiences and newfound bond, they are able to overcome these obstacles.
It could start with Harry having a strange dream about a powerful purple - colored creature. When he wakes up, he starts to notice some odd changes in his Animagus abilities. He might find that he can sense things in a way that's not normal for a wizard or a regular Animagus. Then, one day, he suddenly gets pulled into a portal and finds himself in a world full of Pokémon, where he meets Mewtwo right away.
The fanfiction could center around Genesect and Mewtwo forming an unlikely friendship. Genesect, being a more mechanical Pokémon, might initially be distrusted by Mewtwo. But as they interact, they learn from each other. For example, Genesect could teach Mewtwo about the technology it has, while Mewtwo could show Genesect the power of psychic abilities. It could be a story of mutual growth and respect.
Another plot could be that Voldemort discovers Powergirl's existence and sees her as a threat. He tries to manipulate the wizarding world against her. But Harry and his friends believe in her and together they work to expose Voldemort's lies and also learn from Powergirl about different ways of fighting evil. Powergirl could introduce new concepts of justice and heroism to the wizarding world.
One possible plot could be that Harry discovers a hidden magical realm in the Pokémon world during one of his adventures. There, he meets Rayquaza. Rayquaza, being a powerful Pokémon, senses the strong magic within Harry. Together, they have to fight against a dark wizard who has found a way to corrupt Pokémon and use them for evil purposes in both the wizarding world and the Pokémon world.
Maybe the Timekeeper is actually a descendant of an ancient wizarding family who was tasked with keeping time in balance. In the fanfiction, Voldemort discovers this and tries to use the Timekeeper's powers to go back in time and prevent his own downfall. The Timekeeper has to fight against Voldemort's minions while also trying to find a way to protect the timelines. Harry and his friends get involved when they notice strange time - related disturbances around the school. They join forces with the Timekeeper to stop Voldemort's evil plan.
In a fanfiction, the Triforce could be split among Harry, Ron and Hermione. Harry gets the Triforce of Courage, Ron the Triforce of Power (which he learns to use in a more responsible way), and Hermione the Triforce of Wisdom. Together, they combine their powers of the Triforce with their magic skills to defeat Voldemort once and for all. The Triforce's power could also be used to reform the wizarding world, bringing more equality and peace.
Well, perhaps the magical creatures from the Harry Potter universe end up in the '300' setting. Dragons could be used by the Spartans to fight their enemies. The centaurs could also join the battle, lending their archery skills. And Harry could learn some combat skills from the Spartans, which he could then use back in the wizarding world to fight Voldemort's Death Eaters.
Perhaps in this 'Harry Potter in Vegas' fanfiction, Harry accidentally apparates to Vegas instead of his intended destination. There he meets a group of American wizards who are using Muggle Vegas as a cover for a secret magic convention. Harry gets involved in a mystery where a powerful magical artifact has gone missing and he has to find it before it falls into the wrong hands.
One possible plot could be that the Kubikiribocho, the sword in Naruto, somehow finds its way into the Harry Potter universe. Harry discovers it during one of his adventures in the Forbidden Forest. He initially has no idea how to use it but gradually realizes it has some unique powers that can be harnessed against Voldemort. For example, it might be able to cut through dark magic spells. However, there are also some negative aspects to the sword as it tries to corrupt Harry a bit, just like the influence of the Horcruxes. Harry has to fight against this internal battle while also using the sword's power to defeat Voldemort.