If you really need to have three fandoms crossover (and you need to think very hard about that), then limit the fandoms to as few as possible. You need to balance the fandoms you use. Something like this is like a complex stunt. The pros make it look easy because they know what they are doing. But if you don't know exactly what you are doing, you need to proceed with caution, because when doing stuff like this, it is much easier to go wrong.
So make sure you have someone you trust who you can bounce your ideas off of and make sure you're going the right way, at least one person. Also, be aware of how well two fandoms mix together. Some combinations are odd. And do the research on all of them. This is key. If you have to change something in canon, try to remember the essence.
For example, I found a multi-crossover fic once. One of the categories it was filed under was one of my favorite fandoms, Green Lantern. It was the only one there. No GL characters appeared, ever. I know filing stories like this is hard, but try not to put it in a category where no characters appear. What they did take were concepts, like power rings and the Emotional Spectrum. And the story destroyed them. They used those things so very poorly it defies reason. They failed to understand the essence of any of those things at all. For example, they had OC Mary Sues pick their power ring. Power rings in Green Lantern don't work like that. Power rings, when they are allowed to search with their AI feature, pick YOU because you have the qualities inside needed to literally make them work. To just pick one out like it's a toy or something undermines the idea that what makes the user a superhero are their inner qualities. And it got worse from there. You see what I mean?
Sometimes with crossovers, the crossover can put characters out of their depth. Like a thief who suddenly is caught up in a mess of magic. They don't deal with magic. They don't know how. They feel out of place. Bad stories that want to do that would ignore how out of place they are. A good story might use that feeling of discomfort to their advantage. Another bad thing that happens is that crossovers can make characters seem inferior. Fandom A and B meet. Fandom A is more fantastical, Fandom B, less so. Or Fandom A is more magical and Fandom B is not, and Fandom B cannot deal with Fandom A's problem, and Fandom A does all the work. Both fandoms need to be apart of the story, both need to contribute. Both need to be made equal.
Another flaw of multi-crossovers is the number of characters. They can have way too many if you aren't careful. I remember a Kingdom Hearts story where Pete married Maleficent (Not joking, and they really loved each other... it's like Rita Repulsa and Lord Zedd, except without the love potion). The story included wedding guests from lots of the Disney worlds featured in the games, some worlds not used yet, and other franchises like Power Rangers (I think Disney might have owned the show at the time of writing). And I stopped reading because it was just too much. There were too many characters and the story just lost focus completely.
Then I think of another fic, Of Love and Bunnies. It is a Power Rangers fic. Technically it involves multiple teams, and since that's the same franchise, it's not actually a crossover, technically, but with all the teams making appearances, it functions similar to one. The story is mainly about the romance between two members of the original Power Rangers team, Tommy Oliver and Kimberly Hart. And like I said, each Power Ranger team makes an appearance in the story, large or small, so you have a gathering of tons of characters, with some OCs in there too. It's a humor fic too, and has hundreds of chapters. But it's not as chaotic because while these characters do appear and interact, the story always goes back to the main characters it was meant to be about, and the plot still works around them and how they are effected by everything.
I'm sorry this was so long. I hope this makes sense. It's hard to put into words how multi-crossovers work and can not work, and I tried my best.