One idea could be that Naruto, with his unique abilities like the Rasengan and shadow clones, gets transported to the Mass Effect Andromeda universe. He could use his ninja skills to help the Pathfinder team in combat situations against the Kett or other enemies.
A really interesting plot could be that the jinchuriki in Naruto are somehow related to the Remnant AI in Mass Effect Andromeda. Maybe the tailed beasts have a connection to the technology left behind by the Jardaan, and Naruto has to figure out this connection to save both universes from a new, powerful threat that is emerging.
One idea could be that Naruto somehow gets transported to the Mass Effect Andromeda universe. He might use his chakra powers in unique ways, like using Shadow Clones to outmaneuver the Kett. Another plot could involve Naruto befriending Ryder and teaching them about chakra, which then gives Ryder an edge in combat and exploration.
Perhaps a crossover where the Covenant from Halo discovers the technology of the Milky Way species in Mass Effect Andromeda. This could lead to a power struggle as they attempt to either assimilate or destroy the new civilizations. The story could focus on how Ryder and his crew navigate this new intergalactic conflict while also trying to understand the motives of the Covenant.
A plot could involve a magical artifact from the Harry Potter universe being found in the Andromeda galaxy. The Initiative team discovers it and has no idea what it is. As they study it, they start to notice strange magical effects. Meanwhile, a group of dark wizards from the past who were banished somehow find their way to Andromeda as well and are after the artifact. The Andromeda crew has to team up with a wizard who has been following the dark wizards to stop them.
One idea could be an OC who is a skilled biotic but has a unique way of using their powers, like being able to combine biotics with technology in unexpected ways. For example, they could use biotics to enhance the functionality of a broken piece of alien tech they find in Andromeda.
One interesting Mass Effect Andromeda fanfiction could be about Ryder's further adventures in uncharted regions of Andromeda. Maybe they discover a new alien species that has a unique culture and technology. Another could focus on the relationships between the different crew members on the Tempest, like a deeper exploration of the friendship or potential romance between two characters.
A possible plot is that a Mass Effect technology is introduced to the Naruto universe. Maybe a Mass Relay is found in the Hidden Leaf Village. This could lead to a whole new set of adventures as the ninja try to figure out what this strange technology is and how it can be used. Or, characters from both universes could be combined. Like a Turian with Sharingan abilities.
One idea could be that Naruto is somehow transported to the Mass Effect universe. He could use his ninja skills, like his shadow clones, in combat against the various alien species in Mass Effect. Maybe he teams up with Shepard and they learn from each other's combat styles.
One idea could be that Naruto is somehow transported to the Mass Effect universe and his unique abilities draw the attention of various female characters. They see his determination and power as something new and exciting, leading to a harem situation. For example, characters like Liara might be intrigued by his chakra abilities which are completely different from biotics in their world.
One interesting concept could be the crossover of different species from the Mass Effect universe in unexpected ways. For example, seeing Asari and Krogan working together in a completely new scenario that was not in the original games. Another could be the melding of Andromeda's technology with that of the Milky Way's in unique and creative ways, like a new type of weapon or ship design.
One interesting story could be about a character having to face the challenges of pregnancy while on a dangerous mission in Andromeda. Maybe she has to protect her unborn child while also dealing with alien threats.