One idea could be that the Grey Goo nanobots somehow get introduced into the Mass Effect universe and start to assimilate the technology there. For example, they might start with the Geth, who are already machines, and cause a new kind of conflict. The Reapers could also be affected, maybe the Grey Goo disrupts their harvesting cycle as it spreads uncontrollably.
Perhaps the Grey Goo is created as a weapon by a new, shadowy organization in the Mass Effect universe. It gets out of control and starts to transform planets into a gooey mess. Shepard, or another main character, has to figure out who created it and how to stop it. They could discover that the key lies in some ancient Prothean technology that has the ability to neutralize the Grey Goo's self - replication mechanism.
A plot could involve a character from the Mass Effect series accidentally bringing Grey Goo to a new planet. This leads to the local ecosystem being destroyed as the Grey Goo consumes everything. The character then has to team up with unlikely allies, like a Cerberus agent who also realizes the danger, to stop the spread. They might try to find a way to reverse the Grey Goo's replication process using Mass Effect technology.
Shepard would likely be very determined to stop the Grey Goo. Given Shepard's history of facing threats to the galaxy, they would see the Grey Goo as just another, albeit very different, danger. They would start by gathering information, trying to understand how it works and where it came from.
One idea could be having the XCOM soldiers use their combat skills in the Mass Effect universe. Maybe they are sent to help fight against the Reapers. They could introduce their unique tactics and weaponry to the Mass Effect races.
One idea could be the integration of the mobile suit technology from Gundam into the Mass Effect universe. For example, Shepard's team could discover a lost Gundam unit and try to figure out how to use it against the Reapers. Maybe the advanced beam weaponry of the Gundam could be a game - changer in the fight.
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.
Another plot could involve a shared enemy that exists in both universes. The combined forces of Mass Effect races and Destiny Guardians have to figure out how to defeat this enemy. They would need to overcome their differences in culture and combat styles to be successful.
A great Mass Effect crossover fanfiction idea could be a crossover with the Stargate universe. The Mass Effect races could discover the Stargate network and start exploring other galaxies through it. There could be conflicts and alliances with the various races in the Stargate universe. Also, a crossover with the Dragon Age series might be interesting. The mages and warriors of Dragon Age could interact with the biotics and soldiers of Mass Effect. They could learn from each other's magic and technology, and perhaps even fight together against a dark force that threatens both universes.
Well, a really cool plot could be that the Mass Effect Relay network somehow gets connected to the Crystal Materia in Final Fantasy. This causes chaos as both universes start to blend. Characters from both sides have to figure out how to separate the two worlds again. Along the way, they discover that there are ancient forces at work in both universes that are related. Tali could use her engineering skills to help repair some of the damaged Crystal Materia, while Squall could teach her some sword - fighting techniques from his Gunblade.
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.
Another plot idea is that the Mass Relay network somehow connects to hyperspace lanes in the Star Wars universe. This causes chaos as ships from both universes start popping up in each other's space. A group of Mass Effect characters and a group of Star Wars characters could come together to try and restore order and figure out how to separate the two networks again.
One idea could be that Revan, with his unique combat skills and Force abilities, gets involved in a mission in the Mass Effect universe. Maybe he teams up with Shepard to fight a common enemy that has some sort of connection to the dark side of the Force. Another could be that Revan's knowledge of ancient technologies in the Star Wars universe helps the Mass Effect races to upgrade their own tech, creating new dynamics in their galactic politics.