One idea could be to have the characters from 'House' end up in the world of 'Fruits Basket'. Maybe House could try to diagnose the curse that plagues the Sohma family. His rational and often brusque approach would clash with the more emotional and superstitious aspects of the 'Fruits Basket' world.
In this crossover fanfiction, the Hulk's strength could be used to help the Loud family in a big way. For example, there could be a natural disaster about to hit Royal Woods, like a huge flood or an earthquake. The Hulk, with his superhuman strength, could hold back the floodwaters or stop the shaking ground. Meanwhile, the Loud kids could be helping the townspeople evacuate. It would be a story of how two different universes come together to save a town.
One idea could be that the Loud family somehow gets transported to Gotham City. Lincoln could befriend Robin and they team up to solve a mystery that involves both Gotham and Royal Woods' villains. Maybe the Joker has a plan that involves stealing a special item from Royal Woods, and the Louds have to work with Batman to stop him.
The plot should blend the two worlds well. A good fanfiction will find a way to combine the crime - solving of NCIS with the medical mysteries of House. For example, it could be a case where a Navy person has a mysterious illness that may be related to a crime. The way the story weaves these two aspects together is crucial.
One interesting idea could be a crossover with 'Gravity Falls'. The mystery-solving elements of 'Gravity Falls' could blend well with the magical world of 'The Owl House'. For example, Dipper and Mabel could visit the Boiling Isles and help Luz solve some of the island's mysteries. Another idea is a crossover with 'Avatar: The Last Airbender'. Aang could interact with the magic users in 'The Owl House' and exchange knowledge about different forms of magic and bending. Maybe they could even team up to fight a common enemy that threatens both their worlds.
One way it could work is by having Spiderman visit Royal Woods for some reason. Maybe he's chasing a villain who has some connection to the town. Once there, he meets the Loud family and gets involved in their wacky antics.
One interesting concept could be crossovers with different Disney universes. For example, having characters from 'Frozen' interact with the regular House of Mouse crew. It creates new and unexpected storylines.
One common theme is the clash of different investigative styles. NCIS has its own set of protocols and House has his unorthodox methods. Another theme is the cooperation between two groups of strong - willed characters. And often, there's a medical mystery at the core that ties the two shows together.
One challenge is character integration. The characters from 'Supernatural' have a very different world view and set of skills compared to those in 'House MD'. For example, Sam and Dean are used to dealing with the supernatural, while House and his team are focused on medical diagnosis. So, finding a way to make them interact in a believable way can be tough.
I also like 'When Hunters Meet Doctors'. It shows how the Winchesters would react to the medical world of 'House MD' and vice versa. The story has a lot of action as the brothers deal with the supernatural while also trying to work with the doctors who are skeptical of their claims. It keeps you on your toes as it jumps between the two different storylines.