Well, if 'rim' means the edge or boundary in a more general sense, it could be about girls who explore the edges of a forest, their adventures in finding new paths, and the things they discover near the rims of the forest area. They might encounter unique plants or small animals and have some really exciting experiences.
Your description involves vulgar and inappropriate content, so I can't provide relevant stories.
I'm not aware of any specifically famous 'girls that rim stories' as the term is rather ambiguous. However, there could be stories of girls making a mark in areas like extreme sports where boundaries are pushed. For instance, a girl who was the first to complete a dangerous skateboarding stunt around a large rim - like a circular structure in a skate park. But these are not widely known as a particular genre of 'girls that rim stories'.
I'm not entirely sure what specific 'boy rim on object stories' you mean. It could potentially be about a boy interacting with the rim of an object like a wheel or a cup. Maybe it's a creative or made - up concept for some fictional tales where the boy has adventures related to the rims of various objects.
Another back story might be that of a colonist who was part of a failed utopian experiment. Their colony was supposed to be a paradise, but due to mismanagement, internal conflicts, and external threats, it fell apart. Now, they are in the Rim World, trying to find a new place to call home and start anew.
There could be a Pacific Rim OC fanfiction where the OC is a new pilot. This pilot has a special ability like being able to sense Kaiju movements from a greater distance than normal. The story could revolve around their journey of proving themselves in the face of skepticism from other pilots and commanders in the Shatterdome.
One idea could be that the RWBY characters are Jaeger pilots. Ruby could use her speed and Crescent Rose in the cockpit to fight Kaiju. Another is to have Grimm as a new type of threat in the Pacific Rim universe, and the teams have to adapt their fighting styles.
One idea could be a crossover with the Transformers universe. Picture Jaegers and Transformers teaming up to fight a common enemy. Another could be a crossover with the Godzilla franchise, where the Jaegers have to deal with Godzilla while also facing their usual Kaiju threats. A third idea might be a crossover with the Star Wars universe, perhaps with Jaegers having some sort of technology exchange with the droids or the Jedi using their powers in the context of the Pacific Rim battles.
One interesting fanfiction could be about the backstories of the jaeger pilots. It might explore their lives before they became pilots, like their families and how they were selected. For example, a story could focus on a young pilot who had a difficult childhood but found purpose in the jaeger program.
One idea could be exploring the backstories of the characters more in - depth. For example, fleshing out how Alex became so good at gaming before the alien invasion. Another could be creating an alternate ending where the group doesn't succeed in saving the world right away, but has to embark on a second, more dangerous mission.
One popular 'Pacific Rim fanfiction' story could be about the further adventures of the Jaeger pilots after the events of the movie. Maybe they encounter new and even more powerful Kaiju. Another could focus on the relationships between the different pilots, like a romantic relationship forming between two characters who previously only had a professional bond.