A new villain from another dimension. This villain could be more powerful and cunning than the ones they've faced before. He or she might be after the Powerpuff Girls' powers to use for their own evil plans in their home dimension. Maybe this villain has the ability to manipulate time, which adds a whole new level of difficulty for the girls.
A young scientist from another town. He could come to Townsville for an experiment or research. His scientific knowledge and curious nature would draw the Powerpuff Girls. Blossom would enjoy discussing theories with him, Bubbles would be charmed by his enthusiasm for discovery, and Buttercup would respect his tenacity in the face of difficulties.
One idea could be that the Powerpuff Girls grow older and have to deal with more complex villains who target not just Townsville but the whole world. They might have to learn new powers or upgrade their existing ones to face these threats.
Obviously, Blossom, Bubbles, and Buttercup are the most popular. They are the main characters after all. But villains like Mojo Jojo are also often included as they provide great conflict. Also, the Professor who created the Powerpuff Girls can be an important character in fanfiction, especially if it involves the origin story or some kind of scientific experiment gone wrong.
Professor Utonium is a popular character to include. He is the creator of the Powerpuff Girls and his relationship with them can be explored in different ways in fanfiction. Maybe he creates a new experiment that has unexpected consequences for the girls. Another popular character could be the Rowdyruff Boys as they can create interesting rivalries and storylines with the Powerpuff Girls.
Blossom Z is often very popular. Her leadership skills and strong powers make her a central figure in many stories. Writers like to explore how she makes decisions in difficult situations.
Bubbles is a key character. She has her blonde pigtails and her superpowers. Boomer is also crucial. He has his own set of characteristics that contrast with Bubbles'. In many fanfictions, they are the focus as their relationship is explored, whether it's a friendship that forms unexpectedly or a more complex relationship that develops over time. Other characters from the Powerpuff Girls and Rowdyruff Boys universes may also appear to support or complicate their story, but Bubbles and Boomer are the main attractions.
The Professor is another character that often appears in fanfiction. Writers might explore his backstory more, or they could create scenarios where the Professor has to make difficult decisions regarding the girls' powers or safety. His role as the girls' creator gives a lot of room for interesting plot developments.
Perhaps a jaded detective who has seen too much of the dark side of the city. He starts drinking absinthe to numb the pain. Then he encounters a mysterious informant who also has a taste for absinthe. They start working together on a case and their relationship grows stronger with every glass of absinthe they share.
The Professor could play a bigger role. He could be like a Merlin - like figure, guiding the Powerpuff Girls with his scientific knowledge that has a touch of magic to it. For example, he could create new gadgets for them that are based on ancient artifacts or spells from old books he has studied.
For 'the new sith wars fanfiction', a character like Lyra, a Force - sensitive orphan who was raised by smugglers. She has a natural affinity for the light side of the Force but has a wild and unruly streak. Another potential character is Darth Malice, a new Sith Lord who is extremely cruel and has a vendetta against a particular Jedi family. His actions could drive much of the conflict in the fanfiction.