The Star Wars franchise is a never-ending expanse, but in its decades of success, it remained largely attached to the genre it still defines. But, in the modern day, the franchise has made tentative steps into a couple of other narrative styles.
With The Mandalorian, Star Wars made a valiant and largely successful strut into the venerable western genre. Shortly thereafter, Star Wars: Visions sold itself entirely on the concept of sliding the franchise into the realm of anime. That anthology covered a variety of ideas, from Kurosawa style Samurai to Tezuka-esque charming youth comedy. Those gentle dips into the enormous ocean of genre fiction could open up the franchise for even more new horizons.
Horror
Between the endless monsters that hide in the pits and caverns of Star Wars' galaxy, and the countless powerful villains that commit acts of slaughter, there's plenty to be afraid of. There have certainly been a couple of scary scenes throughout Star Wars media. Perhaps the most interesting comes in the sixth episode of The Mandalorian.
Entitled "The Prisoner," that episode makes the titular Din Djarin something akin to a high-tech slasher movie villain. The set design, lighting, and violence on display in that single episode came across like a short horror scene in a larger narrative. The power of clean white walls and futuristic technology as a medium of horror is clear and well established.
A full-fledged Star Wars horror film could be incredibly powerful. Whether it's a stripped-down space survival story like Alien, a darker take on the force ghost concept, or perhaps the grim tale of the PTSD-riddled survivors of the Clone Wars. There are nearly endless possibilities because the main difference between action and horror is framing. A horror story is often just an action story with a weaker main character, so putting regular people up against a Sith warrior could be a fascinating horror tale. The villains of Star Wars are always powerful, but rarely scary. The franchise could benefit from trying to evoke fear rather than its typical hope.
Romance
Most Star Wars movies have a romance subplot, and most of them are terrible. Whether it's the accidental light incest of Luke and Leia in A New Hope, the painfully awkward dirge of Anakin and Padme, or the unpleasantly violent back and forth of Rey and Kylo, it just doesn't work often. Instead of adding to the narrative, this aspect of the narrative is typically distracting at best and disgusting at worst. There are exceptions: Han and Leia have an interesting relationship that changes with the decades, but the majority would leave the films better for their absence. If Star Wars attempted to make a full love story, the results could lend new dimensions to the beloved galaxy.
Imagine star-crossed lovers attempting desperately to reach each other despite being conscripted into competing Empire and Rebel armies. A Romeo and Juliet tale set in space, with the added complexities of the intricacies of the galactic conflict could be very special. Alternatively, the idea of Anakin's love interest with Padme is strong, despite its abysmal execution.
The concept of a Jedi struggling with their vows against a whirlwind romance could carry an entire story, but instead, it's a minor element of a larger narrative. A love story set in the Star Wars universe could carry a variety of unique dimensions while allowing the audience to see a rare moment of tenderness in an often war-torn galaxy. The audience for the average Star Wars film might not have a ton of crossover with the average serious romance, but it could open up the franchise to new fans.
Comedy
There isn't anything Star Wars tries and fails at more frequently than landing a joke. Bits fall flat left and right throughout the prequels and the newest trilogy. The more subtle humor of the first two films land more regularly, but Return of the Jedi went downhill in that department. Entire characters are dedicated to jokes, but only a few one-liners and random bits elicit a chuckle from the fans. Often too mired in references or immature slapstick to be funny, Star Wars' approach to humor is one-note and could stand to learn some new tricks.
There are infinite vectors for a full comedy set in the Star Wars universe. Comedies set in the military are everywhere, ditto police departments, fire departments, hospitals, and many more intense settings. The franchise makes constant jokes out of the villainous stormtroopers, despite their extremely grim real-world inspirations.
A Stripes or MASH-inspired comedy set in the imperial army would be an easy glimpse into this world of enjoyable incompetence. Alternatively, the openness of the galaxy and the constant war must give way to armies of satirists. A parody of Star Wars, set inside its universe could be a genius work of incisive comedy. The Star Wars universe is unfunny far too often, so perhaps putting that angle front and center could fix its problems.