Another plotline might involve a backstory for one of the villains. In the 'a good day to die hard fanfic', it could explore how the main villain got involved in the criminal underworld and what his motives are beyond just the obvious. This could add more depth to the conflict between him and McClane.
A third plotline could be a family - centric one. Since family is often a theme in the Die Hard series, the fanfic could focus on McClane's relationship with his family during the events of the story. Perhaps his daughter gets involved in the situation in an unexpected way, and McClane has to protect her while also dealing with the main threat.
One possible plotline could be an alternate version of the events in the movie. For example, John McClane could have a different set of challenges or allies. Maybe he teams up with a local detective who has unique skills and together they take on the bad guys in a more strategic way.