A good crossover could be that the devils in Highschool DxD make a deal with the forces of Hell in Spawn's world. As a result, Spawn is sent to oversee the deal. He ends up getting caught in the middle of the power struggles between the devils, angels, and fallen angels in Highschool DxD. His presence would disrupt the balance and create new alliances and rivalries.
One idea could be that Spawn somehow gets transported to the world of Highschool DxD. He could end up being a mysterious new student at the school. His powers and dark nature would contrast with the more flamboyant and magical powers in the Highschool DxD world. Maybe he'd get involved in the battles between the different factions, using his chains and hellish powers in a way that no one in that world has ever seen before.
Another crossover idea is that a character from Highschool DxD, like Issei, accidentally summons Spawn instead of a devil. Spawn then has to deal with the chaos of the Highschool DxD world while also trying to find a way back to his own. He might teach Issei some new combat techniques that are a mix of his own and what he's learned from fighting in his world.
If Spawn were to interact with the main characters, he would bring a whole new level of seriousness. He has a dark past and a lot of baggage. When it comes to Issei's goal of becoming a harem king, Spawn might find it absurd but also interesting in a way. He could offer his own perspective on power and how to use it responsibly, which would be a contrast to the more carefree attitude of some of the Highschool DxD characters. And with the other characters like Akeno and Koneko, he'd be sizing them up, trying to figure out if they're threats or allies.
One idea could be that the characters from Highschool DxD end up in the Hellsing universe. Maybe Issei and his friends are mistaken for new types of vampires due to their devil powers. They then have to team up with the Hellsing organization to clear their names and also fight against a common enemy that is threatening both the devil and human worlds in this combined universe.
A third idea is that there's a mix - up with the curses in both worlds. Ranma's curse of changing into a girl when splashed with cold water gets combined with some of the magic in Highschool DxD. This creates a whole new set of problems and adventures for him as he tries to figure out how to deal with this strange new situation while also trying to keep his identity a secret from the new characters he meets.
There's a crossover that combines Highschool DxD with the Naruto universe. In this fanfiction, the ninjas' skills are pitted against the devils and angels of Highschool DxD. It's a fun read as it explores how the different power systems would interact. The author does a great job of keeping the characters' personalities intact while introducing new and exciting storylines.
Yes, there are some. You can start by looking on fanfiction websites like FanFiction.net or Archive of Our Own. Just search for 'khr crossover highschool dxd' and you'll likely find a variety of stories.
One interesting Issei crossover fanfiction could be where he crosses over into the world of 'Fate/stay night'. In this scenario, Issei's devil powers might interact in unique ways with the Servants and magic in the 'Fate' universe. Another could be a crossover with 'Naruto', where Issei has to face the shinobi world with his devil abilities. There are also some crossovers where he goes to the world of 'One Piece' and has to deal with pirates and Devil Fruits while still having his own devilish powers.
One idea could be a crossover where Naruto characters attend the Highschool DxD academy and interact with the Espada. For example, Naruto's determination could inspire the DxD characters to face their challenges more bravely. The Espada's powers could create interesting battles and power dynamics within the school setting.
Maybe in the fanfiction, the Campione characters are invited to the Highschool DxD world to participate in a special tournament. They bring their own unique skills and knowledge, and during the tournament, they form unexpected alliances with the devils, angels, and fallen angels. This would allow for a lot of character interactions and development.
One idea could be that Naruto characters attend the Highschool DxD academy. For example, Naruto himself could be a new student with his unique ninja skills. He might form an unlikely friendship with Issei. Another idea is a battle tournament where ninja techniques are pitted against the devilish powers in the DxD world.
One idea could be to cross it with a magical girl anime. The main character from Highschool DxD could find himself in a world full of magical girls and form a harem with them. They could fight together against common enemies while also dealing with the typical harem situations like jealousy and misunderstandings.