Another theme could be exploring the backstories of the other characters in the Grease universe. Like how Rizzo got to be the tough girl she is, with fanfiction delving into her family life or early experiences in high school that shaped her.
Sandy is also a popular choice. Her transformation from the innocent new girl to a more confident young woman gives a lot of room for creativity in fanfiction. Writers can expand on how she adapts to the new environment and her relationship with Danny in more depth.
Grease science fiction might be a very niche or even newly - coined term. It could refer to science - fiction stories that involve machinery or mechanical elements that are 'greasy' in the sense of being industrial and mechanical. Think of a story set in a steampunk - like world where the gears and engines are constantly greased, and this aspect of maintenance and the properties of grease play into the plot, such as a malfunction due to a lack of proper greasing causing a spaceship to be in danger.
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.
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.