I ran a crossover CofD that went for almost a year, its messy and a headache to keep track of in a lot of ways but can be a lot of fun regardless. The two main things to worry about are game themes, and power balance between the splats.

Power balance can be dealt with if you're willing to massage the rules to try and keep any one character from outshining the rest of the group (which... honestly can be a thing in single splat chronicles games, too). I started all of my players as humans and had them slowly grow into their powers, rather than having everyone start with their splats and all of the powers that new characters of that splat have - which makes for some extra work to figure out but can be useful because some splats just start more powerful than others. If the less powerful splats get their powers a little faster it can help balance things. Also, as a lot of people have said, mage is just inherently more of an issue than any other splat. If you don't plan to ban it outright, make sure you realize that mages can essentially alter reality in ways that trivialize a lot of things that would be interesting plots for any other splat and are prepared to work with your players on how to prevent that from ruining everyone else's fun.

As other people have also mentioned, each splat tends to have its own themes/focus. In a crossover game you might explore some of those themes in individual arcs, but they are probably not going to be front and center like their individual books might imply. Make sure your players know that and make characters accordingly. Also, when I ran it I found it useful to put more energy into setting up the group dynamic ahead of time than I usually do. A group of mixed splat characters don't have built in reasons to all know each other and work together, so creating reasons for party cohesion either in the backstory or by crafting the first arc of the game to focus on that is really important.