One way to develop their relationship uniquely is to give them a shared dream or vision. Every time they sleep, they enter the same dream world where they can talk and interact without the constraints of the real Twilight world. In this dream world, they gradually learn more about each other's deepest desires and fears, which then influences how they act towards each other in the real world.
Their relationship could be developed uniquely by having them communicate through a special form of magic that only they share. This magic could be tied to their emotions, so when they're happy, it creates beautiful glows, and when they're sad, it sends out a signal that only the other can understand.
Their relationship could be developed through a shared mission. For example, they are both tasked with protecting a special, ancient artifact that has the power to bring peace to their world. Working towards this common goal, they gradually learn to respect each other's abilities. Alec might be impressed by Seth's loyalty to his pack, and Seth could come to admire Alec's strategic thinking as a vampire.
Maybe Carlisle and Bella could bond over their shared experiences of being different from the norm. Carlisle is a 'vegetarian' vampire, and Bella is a human who is in love with a vampire. They could have deep conversations about how they both struggle to fit in with their respective worlds and find solace in each other's understanding. This would add a new layer to their relationship and make it more unique.
One way to develop their relationship uniquely is to put them in a situation where they have to protect each other's secrets. For example, Jasper might have a secret from his past as a vampire in the military, and Bella has her own secrets about her relationship with the wolves. By relying on each other to keep these secrets, a strong bond forms between them.
Their relationship could develop uniquely if Rachel takes on a teaching role for the younger glee club members under Will's guidance. This role reversal would force them to see each other in new lights and create a deeper bond.
A unique way to develop their relationship could be through a series of challenges. For example, they are trapped in a mysterious dimension together and have to rely on each other to escape. In the process, they discover each other's strengths and weaknesses, and Kurama realizes that Kushina is not just Naruto's mother but a powerful ninja in her own right. This mutual respect and reliance would strengthen their relationship.
Their relationship could be developed uniquely by having them start as enemies in a sense. For example, Sephiroth could be on a mission that Aerith unknowingly gets in the way of. But instead of killing her immediately, he's intrigued by her. This initial encounter could spark a series of events where they keep crossing paths. Each time, they learn a bit more about each other. Maybe Aerith starts to see the pain behind Sephiroth's cold exterior, and Sephiroth begins to respect Aerith's strength and determination. Over time, this could lead to a complex relationship that is part friendship, part something more, as they both struggle with their own destinies and how the other fits into it.
Another way to develop their relationship uniquely is if Aipom gets a prophecy about a great danger that Ash will face in the future. Aipom decides to secretly train itself extra hard to be able to protect Ash. When Ash finally discovers what Aipom has been doing, he is touched and their relationship becomes even stronger. This would show a different side of their relationship, with Aipom being the protector instead of the one usually being protected by Ash.
Their relationship could be developed through a shared love of transfiguration. Hermione could seek out McGonagall for extra lessons and in the process, they bond over the beauty and complexity of the subject.
One way would be if they were both transported to a different dimension. In this strange new place, they have only each other to rely on. They would need to figure out how to survive and find a way back home. This shared struggle would bring out different sides of their personalities and force them to trust each other completely, thus developing their relationship in a very distinct way.
Their relationship could be developed uniquely by having them swap powers for a day. This would force them to understand each other on a whole new level. For instance, Draculaura would have to deal with Clawd's werewolf instincts and Clawd would have to adapt to Draculaura's vampire abilities. It would create a lot of comical and also some very heartfelt moments as they support each other through the challenges.