Some fanfics might center around romantic relationships within the group or between the Pink Ladies and other characters. These can add a new layer of depth to the story, showing how the characters interact on an emotional and romantic level, which can be really engaging for fans of the show.
Create an interesting plot. It could be something that fills in the gaps in the show's story or takes the characters on a new adventure. For example, you could have the Pink Ladies deal with a mystery that has to do with their school's history. Also, make sure your writing has good pacing. Don't rush through important events, but also don't drag out uninteresting parts.
You can start by looking on fanfiction websites like Archive of Our Own (AO3). It has a large collection of various fanfictions, and you might be able to find some that combine Twilight and Grease in a singing - related context.
One interesting story could be where the characters from Twilight are transported into the Grease universe and they start singing the classic Grease songs in their own unique ways. For example, Bella might sing 'Summer Nights' with a different kind of shyness compared to the original characters in Grease.
The story of Grease focuses on the clashes and connections between different social groups in high school. It's filled with catchy songs and memorable characters. Danny and Sandy's relationship undergoes various ups and downs as they navigate the challenges of adolescence and trying to fit in.
Grease is purely fictional. It was crafted by writers and composers to provide an enjoyable and lighthearted musical experience. There's no real-life basis for the story or its characters.