I travel with 5 tier cakes all the time. I do a few extra things, but for the most part they travel just the same as regular cakes. What’s the base tier size… 16/18”? I will take a MDF board and then hot glue a same-sized cardboard cake drum on top of it and wrap both in cake foil. Once I finish the cake, I will run a sharpened dowel through the center of the entire cake. That cake drum gives the dowel something to bite into.
Cakes that big I usually don’t put in a box, I just put them on a piece of rubber shelf liner so they don’t slide. Just make sure you have enough help to carry all that cake once you get to the venue! :)