I work on Windows with a Mac designer using Dropbox all the time.
You are not going to be able to do this with everyone on different versions of InDesign so you need to fix that before you go any further.
So if I get everyone on the same version of inDesign (CC, for example), it will work?
As if you were all sitting in the same room.
Fair warning…the lock files don’t work on Dropbox so you do have to be aware of someone working on the file. You may want to break it up into sections.
I'd strongly recommend subdividing. If people are working on separate pages, divide the document into pages. If they are working on portions, then create documents with single articles or portions. Make it a single person's responsibility to assemble the parts. The pain of losing edits because two people try to work at the same time (AND THEY WILL) is far worse than the pain of subdividing, and it will happen of course when you are under pressure.