One idea could be a story where a group of Destiny guardians somehow end up in the Hive's territory and have to fight the Taken while also trying to understand the Hive's motives. They could form an uneasy alliance with some Hive members who also see the Taken as a threat.
Maybe in the fanfic, a Destiny character gets Taken but retains some of their own consciousness. They then use their newfound powers and knowledge of the Destiny universe to try and stop the Taken from spreading further. This could involve some really cool battles and power struggles within the Taken ranks.
First, do some research on both Destiny, the Hive, and the Taken. Know their characteristics, powers, and the lore behind them. Then, come up with a basic plot idea like how the two universes will interact. For example, it could start with a portal opening between their worlds.
A Destiny 2 and Mass Effect crossover fanfic would be cool. The Guardians could interact with the various alien species in the Mass Effect universe. They could exchange knowledge about their different forms of space travel and combat tactics. For example, the Guardians could show the Mass Effect characters how to use their Light abilities in battle.
One idea could be that the Master Chief from Halo is transported to the Destiny universe and has to team up with a Guardian to stop a new threat that is using technology from both universes. For example, the Covenant and the Fallen might be working together under a powerful new leader.
One idea could be to cross Naruto with another popular anime like One Piece. Naruto characters could end up on the Grand Line, facing pirates and searching for the One Piece while using their ninja skills. Another idea is to cross it with a fantasy series like Harry Potter. Picture Naruto and his friends attending Hogwarts and learning magic alongside their ninja training. Or perhaps a crossover with the DC Universe, where Naruto characters gain superpowers similar to the DC heroes and fight against villains in a new, urban setting.
One idea could be to have the Guardians from Destiny encounter the Normandy crew in Mass Effect. They could team up to fight a common enemy like a new, powerful alien race that has the technology to disrupt both the Traveler's Light in Destiny and the Mass Relay network in Mass Effect.
One idea could be to have the characters from Harry Potter interact with the Guardians from Destiny in a battle against a common dark magic - influenced enemy. For example, Harry Potter could team up with Cayde - 6 to fight off a horde of Death Eaters and Fallen that have somehow merged their powers.
One idea could be that the characters from RWBY are transported into the Destiny universe and have to learn to use the unique weapons and powers there. For example, Ruby could be fascinated by the Exotic weapons in Destiny and try to incorporate their technology into her Crescent Rose. Another plot could involve the Guardians from Destiny being sent to the RWBY world to help fight against the Grimm. They would have to adapt to the new environment and team up with the RWBY characters. The third idea is that a powerful enemy from the Destiny universe somehow crosses over to RWBY's world and the combined forces of both universes have to stop it.
Maybe in this crossover, Naruto has a vision of the Traveler from Destiny. Curious, he somehow manages to cross over to the Destiny universe. There, he meets the different classes of Guardians. He could learn about their weaponry and powers and in turn, teach them about chakra. They could then work together to stop a Vex invasion that is spreading across both universes.
One idea could be having the Guardians from Destiny team up with the Jedi in Star Wars. The Guardians' unique abilities with their Light powers could interact in interesting ways with the Force used by the Jedi. Maybe they could face a common enemy that threatens both their universes, like a powerful Sith who has somehow gained access to the Darkness from Destiny.
One interesting idea could be exploring an alternate destiny for Harry. Maybe he becomes a Slytherin instead of a Gryffindor. This would completely change his relationships and how the story unfolds.