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.
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.
In a Prototype - Mass Effect crossover fanfiction, a possible scenario is that the Reapers from Mass Effect encounter Mercer. Since Mercer can consume and assimilate other beings, it would be interesting to see how he'd fare against the Reapers. He might be able to absorb some of their technology or even gain new powers from them. And the way the different races in Mass Effect, like the Turians or Asari, would react to his presence would also be a great plot point.
Another aspect could be the exploration of the political and cultural differences between the two universes. XCOM is mainly focused on Earth defense, while Mass Effect has a complex galactic political system. A fanfiction could explore how the two groups interact when it comes to things like trade, alliances, and dealing with common threats. For instance, how would the XCOM Council (if there was one in the crossover) deal with the Citadel Council's decisions and vice versa?
A great concept could be a story where the Prototype technology is somehow introduced into the Mass Effect universe. For example, some Cerberus scientists could get their hands on Prototype samples and start experimenting. This could lead to the creation of new, dangerous hybrids that the main characters have to deal with. Or perhaps Shepard has to team up with a character similar to Mercer to fight a common enemy that is exploiting both Prototype and Mass Effect technologies.
One idea could be the Pilots from Titanfall teaming up with the Normandy crew in Mass Effect. They could share their combat skills and technology. For example, the Pilots' parkour abilities might amaze the Mass Effect characters, and in return, the advanced biotics and tech of the Mass Effect universe could be useful for the Titanfall side.
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 to have Shepard from Mass Effect end up in Thedas (the world of Dragon Age). Maybe Shepard's skills and technology could be misinterpreted as some sort of magic or ancient power. Another could be that a group of Dragon Age characters stumble upon a Mass Relay and end up in the Mass Effect galaxy, having to deal with different species and technology there.
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.