Well, perhaps it could be about Beast Boy losing control over his powers and fully becoming the beast all the time. Maybe there's a curse or some dark magic at play that forces him into this state.
The fanfic could start with Beast Boy being exposed to some sort of mutagenic substance. This causes his shape - shifting abilities to go haywire and he becomes the beast permanently. He then has to adapt to living like this. He might be shunned by society at first, but gradually find others like him or learn to control the beast within in a new way. The story could also explore how he uses his new, more powerful and wild form to protect the city in a different manner than he did before as a Teen Titan.
It could be a mad scientist who wants to study Beast Boy in his beast form and keep him caged for experiments.
The plot could involve Raven feeling more isolated than usual and retreating into her 'lonely beast' form. Beast Boy, noticing this, decides to try and help her. He might start by just being around her, and gradually they start to communicate more. Eventually, they could face a common enemy together while Raven is still in that form, and their combined efforts lead to a stronger relationship.
One possible plot could be that Beast Boy gets angry because his friends don't trust his new animal form discovery. He feels isolated and lashes out at them, causing chaos in the Titans' tower. His anger might lead to him running away and getting into trouble in the city, where he has to face his emotions and learn to control his powers better while his friends search for him.
One possible plot could be that Beast Boy fails to save someone he cares about deeply. This guilt and the sense of loss could be the source of his sadness. He would then struggle to come to terms with his failure and find a way to move forward.
Perhaps in the fanfic, Beast Boy going into heat could lead to him having a stronger connection to his animal instincts. He might start to have dreams or visions related to his animal forms. This could then lead to a story where he has to go on a journey to understand this new part of himself. His friends could be worried about him and try to follow, but he may want to do it alone at first.
One possibility could be that Beast Boy feels out of place. Maybe he's constantly overshadowed by the other Titans and decides he can be more effective on his own. He might leave to explore his identity outside of the team and find his true purpose in a world where he doesn't have to conform to the Titans' way of doing things.
As I'm not familiar with this particular fanfic, the plot could be a million different things. It could be a love story where Beast Boy finds his true love. Or it could be an adventure where he discovers the true nature of his powers. It might also be a story about him growing and maturing, learning what it really means to be a hero, which is a way of becoming 'true' to his heroic self. Fanfics often take the original characters and put them in new and unexpected situations, so this one could be quite creative in its plot development.
It could be that Beast Boy is actually undercover as Slade's apprentice. He might be trying to gather information to take Slade down from the inside. This would add an element of mystery to the fanfic. He would have to pretend to be on Slade's side while secretly working against him, which would require a lot of acting skills on Beast Boy's part.
It could be Slade. Slade might manipulate situations to make Beast Boy look bad in front of his friends. He could spread false rumors or set up situations where Beast Boy fails, which would make Beast Boy angry at being wrongly accused and at the fact that his friends might start to doubt him.
He might gain the power of enhanced healing. So not only can he transform into different animals, but if he gets injured during a fight or accident, he can heal himself much faster than before. This would make him even more of a formidable hero in the fanfic's story line.