One great Klaus 'Umbrella Academy' fanfiction is 'The Ghostly Encounters of Klaus'. It delves deeper into Klaus's relationship with the spirits he can see and communicate with. It adds more emotional depth to his character.
There's also a fanfic called 'Klaus and the Mysterious Artifact'. In this story, Klaus stumbles upon an ancient artifact that seems to have a strange connection to his family's past. It's full of adventure and mystery, and the author does a great job of writing Klaus' character as both humorous and complex.
Well, Klaus and Dave's relationship in the fanfiction can be quite different from the show sometimes. Some fanfictions might focus on their backstories together, like how they first met. Others could explore what might have happened if Dave had survived. It really depends on the author's take, but generally, it's a relationship full of love and the struggle to be together given all the obstacles in the Umbrella Academy universe.
A possible plot idea is that Klaus discovers that his ghost - seeing ability is not just a random power, but part of a much larger, supernatural plan. The ghosts he sees are actually messengers from a different dimension, and they are trying to guide him to save both his world and theirs. Also, the fanfiction could explore a plot where Klaus' relationship with a particular ghost deepens into a strange friendship. This ghost has the ability to enter the dreams of the other Umbrella Academy members, and Klaus has to use this to his advantage to solve a mystery within the academy. Or, there could be a story where the ghosts start to disappear one by one, and Klaus has to race against time to find out what is causing it and stop it before he loses his connection to the spirit world completely.
A unique plotline could be Klaus training a new group of people with powers similar to his. It shows his growth as a character from being a bit of a mess to someone who can mentor others. This often involves him sharing his own experiences and how he learned to control his powers better.