There are quite a few. A great one might involve Morticia Addams' gardening skills being used to grow some very strange and magical plants in the Hogwarts greenhouse. The Addams family values of being different and unafraid of the dark side could be a great contrast to the more 'normal' wizarding families in the Harry Potter series. This can create a lot of interesting storylines, like how the Addams kids deal with the rules and traditions at Hogwarts.
Imagine Pugsley Addams getting a Hogwarts letter. He'd be so excited to learn magic, especially dark magic. He could get into trouble by trying to create his own spells inspired by the Addams family's unique interests. Meanwhile, the Addams family's butler, Lurch, could be a half - giant like Hagrid. He could interact with Hagrid and they could share stories about taking care of strange creatures.
A great plot could be a duel between Harry and Wednesday. Harry uses his wizarding spells while Wednesday uses her unique skills of dealing with the spooky and unexpected. It would be a battle of two very different kinds of power. Another plot could be a quest where they both search for a lost magical artifact that has the power to bring out the darkest secrets of both their worlds. They have to overcome many obstacles together, like strange creatures and dark magic spells.
In some fanfictions, there could be a plot where the dark magic in the Harry Potter universe intersects with the Addams family's natural inclination towards the macabre. Maybe a dark wizard tries to use the Addams family's home as a base for some evil plan. But the Addams family, with their own brand of strength and eccentricity, turn the tables on the wizard. This could lead to an alliance between the Addams family and the Hogwarts faculty to fight off the common threat.
A possible concept is that of a Hogwarts student who discovers they are related to the Addams Family. This student could bring some of the Addams' values and aesthetics to Hogwarts. For example, they might decorate their dormitory in a more gothic and spooky way, much to the bewilderment of their roommates. They could also introduce some of the Addams' unique forms of 'entertainment' like their strange and macabre family games. And it would be interesting to see how the teachers at Hogwarts react to this new addition with their Addams - like quirks, especially when it comes to classes like Defense Against the Dark Arts, where the student's view of 'dark' might be a bit different from the norm.
A fanfiction could be set in a world where Hogwarts has an exchange program with Nevermore Academy (Wednesday's school). Harry Potter is chosen to go to Nevermore, and Wednesday is sent to Hogwarts. At Hogwarts, Wednesday has to deal with the magical chaos and the rather more optimistic students compared to her own schoolmates. Meanwhile, Harry has to navigate the strange and often macabre world of Nevermore, and they both learn a lot from each other's worlds.
One idea could be that the Addams family visits Hogwarts. Wednesday could be intrigued by the Dark Arts classes and start causing some spooky chaos among the students. She might even try to out - do Draco Malfoy in being menacing.
In a fanfiction, Wednesday Addams could visit Hogwarts. She would probably find the castle fascinating, but also a bit too cheery in some parts. She might make friends with some of the darker - themed students, like those from Slytherin. And she could introduce them to her pet spiders and other creepy - crawlies. Harry would be intrigued by her and her family's attitude towards death and the afterlife, which is different from what he has learned in the wizarding world.
A possible crossover could be in the area of magic. The Addams family might have their own brand of 'weird' magic that clashes or combines with the magic in Harry Potter. For instance, Pugsley Addams could create some really odd potions using ingredients from both the Addams' world and Hogwarts' supply.
Another plot could be that Wednesday discovers a hidden connection between her family's dark past and some of the ancient, forgotten magic in the Harry Potter universe. For example, her family might have had some interaction with a dark wizard in the past that has now led to a curse on Hogwarts. Harry and Wednesday then have to work together to break the curse. Wednesday's no - nonsense attitude and knowledge of the darker side of things could be a great asset in this adventure.
The Addams family could fit into the wizarding world by bringing their own sense of style and values. Their mansion could be a place where students go for a different kind of magical experience. They might hold parties where they showcase their strange magical artifacts. In terms of the Hogwarts houses, they might not fit the typical mold. Wednesday could be a unique Slytherin who doesn't care about the pure - blood - mania but rather about her own personal power. Pugsley could be a Hufflepuff who is loyal to his family's odd ways. And the family as a whole could contribute to the diversity of the wizarding world.