Perhaps in the fanfiction, Voldemort teams up with some of the Justice League's villains. This would force the heroes from both universes to work together. The wizards could teach the superheroes about magical defenses, and the superheroes could share their combat and strategic skills. Also, imagine Hermione tutoring Batman on advanced magical theories. It would be really cool to see how their different worlds' knowledge would interact.
One idea could be that Harry Potter is magically transported to the DC Universe and is mistaken for a meta - human. The Justice League initially views him with suspicion but then realizes his unique magical abilities could be an asset in fighting a new, magic - based threat.
Imagine a scenario where a young wizard from the Harry Potter world, who has a natural ability to open portals, accidentally opens a gateway to the world of the Justice League. However, this also attracts the attention of Silent Hill. The League and the wizards have to work together to close the portals and keep Silent Hill's nightmares at bay. The wizards can use their spells and the League can use their superpowers to fend off the encroaching darkness.
Another concept is that the magic from the Harry Potter series starts to seep into the DC universe where the Justice League operates. This causes chaos as the laws of physics in the DC world are disrupted. The Justice League has to seek help from Hogwarts professors to understand and contain this new form of magic energy. Superman might be intrigued by the idea of magic being a new power source or a new threat he can't easily overcome with his super strength.
A really cool crossover concept could be a combined threat that requires both the skills of the Justice League and the magic of the Harry Potter world to defeat. Maybe a powerful alien sorcerer arrives on Earth. The Justice League's superpowers alone aren't enough, so they team up with Harry Potter and his friends. Harry could use the Patronus charm to fend off the dark magic of the alien, while the Flash could use his speed to quickly deliver magic items to different locations as needed.
One interesting crossover could be Harry using his magic in the world of the Justice League. For example, he could use spells like 'Accio' to retrieve important items during a Justice League mission. Maybe he'd team up with Superman and use magic to enhance Superman's powers in a unique way.
In a 'Harry Potter Harem Justice League Fanfiction', it could start with Harry being transported to the Justice League's universe. He discovers that his magic is a unique power there. The harem might form as the female members of the League, like Hawkgirl and Black Canary, are intrigued by this new 'wizard' in their midst. Meanwhile, they all figure out that an old enemy of the League has teamed up with Death Eaters from Harry's world. So, they train Harry in their ways and he teaches them some magic, all while dealing with the budding relationships.
Maybe a story where some of the younger members of the Young Justice team are frustrated with the Justice League's methods and decide to take on a mission on their own, but end up getting in over their heads and have to call in the League for help. This could lead to a lot of character development and some interesting dynamics between the two groups.
One idea could be a crossover where the Young Justice team has to team up with the Justice League to face an interdimensional threat. Maybe a powerful villain from another dimension is trying to invade Earth and the combined skills and powers of both groups are needed to stop it.
Yes, there are quite a few. You can start by looking on fanfiction websites like Archive of Our Own or FanFiction.net. Just search for the key terms 'Harry Potter Justice League Harem' and you'll likely find some interesting reads. However, the quality can vary greatly, so it might take some time to find one that really suits your taste.
One idea could be Izuku getting accidentally transported to the Justice League's universe. He could then use his unique Quirk to help the Justice League in a battle against a powerful new villain that they're having trouble with. For example, his One For All power could give him the strength to hold back a giant monster while the League figures out a more permanent solution.