Perhaps the alliances have started to cause more harm than good. Maybe they are creating political unrest within the wizarding world. Harry, being the hero he is, realizes this and cancels the alliances to restore peace and order. He might face a lot of opposition at first, but he stands his ground for the greater good.
In the fanfiction, it could be that the alliances are actually fronts for some sort of mind - control experiment. Harry stumbles upon this information and cancels the alliances to free those who are being unknowingly manipulated. He then has to deal with the consequences of breaking these powerful alliances, which could include making new enemies and having to find new ways to protect himself and his friends.
One possible plot could be that Harry discovers some dark secrets about the alliances. For example, he might find out that an alliance is being used by a dark wizard to infiltrate Hogwarts. So, in order to protect the school and his friends, he decides to cancel the alliance.
Maybe the main antagonist is a dark force that has been slowly taking over the alliances from within. Harry notices this and decides to cancel the alliances to prevent the dark force from spreading further. This dark force could be something like an ancient evil that has awakened and is using the alliances as a way to gain a foothold in the wizarding world.
Well, perhaps in the fanfiction there is a power struggle within the alliance. Harry, being a central figure, might not want to be part of a group where there is constant jockeying for power. Also, new revelations about the alliance's past actions or connections could make Harry want to distance himself. For instance, if he finds out the alliance has some shady dealings with dark wizards in the past, he would surely break the alliance to protect his own integrity and that of his true friends.
Well, perhaps the Yautja is on a hunt in its own world but gets caught in a magical portal that leads it to Hogwarts. The students are both scared and intrigued. Hermione starts researching about it, trying to find a way to send it back. Meanwhile, the Yautja sees the Death Eaters as worthy prey and starts stalking them. Harry has to convince the Yautja not to go on a full - out killing spree which might endanger innocent lives as well.
A possible plot could be that a Smilodon escapes from a magical menagerie in the Forbidden Forest. Harry and his friends discover it and try to return it safely without getting hurt or getting in trouble with the Hogwarts authorities.
Perhaps Harry could be a wizard - geisha hybrid. He might use his magic to enhance the traditional geisha arts, like creating magical illusions during his performances. He could be in a Hogwarts - like school but also trained in the ways of the geisha, with spells and potions being used in the context of geisha traditions.
Well, one possible plot could be that Orochimaru somehow finds his way into the Harry Potter universe. He might be interested in the unique magic there, like the Elder Wand or the Philosopher's Stone. He could try to use his ninja skills and devious ways to steal these powerful magical items, and Harry and his friends would have to stop him using their own magic.
In this 'harry potter math fanfiction', it might also be that there is a new subject in Hogwarts called 'Magical Math'. The teachers could be magical creatures who are experts in both magic and math. The students would have to learn things like how to use equations to create spells or use geometric shapes to build magical structures. And there could be a big competition where the students use their math skills to win a great prize, like a magical artifact that can enhance their magic power.
A possible plot could be Morgoth's return in a weakened form in the Forbidden Forest. His presence starts to corrupt the magical creatures there. Harry and his friends sense the disturbance and go to investigate. They soon realize it's a much greater threat than they thought and must find a way to either banish Morgoth back to his realm or destroy his essence completely.
Well, perhaps in this fanfiction, Harry Potter uses his magical skills in the context of auditing. He could use spells to detect financial irregularities, like a magical version of auditing software. For example, he might cast a spell that reveals hidden transactions in a company's books.
One possible plot could be that Harry and Ginny go to a secluded wizarding cottage by the sea. They spend their days exploring the nearby magical creatures and hidden coves. At night, they sit by the fireplace and share stories from their Hogwarts days, strengthening their bond even more.