In a fanfiction where Spider - Man joins Black Cat, it could also explore their relationship on a deeper level. They might start to understand each other's motives better. For example, Black Cat's more morally ambiguous actions could be challenged by Spider - Man's sense of justice, leading to some interesting character development for both of them. And they could use their unique abilities, Spider - Man's web - slinging and super strength and Black Cat's agility and thieving skills, in creative ways to solve problems.
One possible scenario in this fanfiction could be that Spider - Man and Black Cat team up to take on a new supervillain in the city. Maybe it's someone who has a personal vendetta against both of them, and their combined skills are needed to stop the bad guy.