There is not a way right now for students to collaborate in the way to described. They can "import" screens from other projects which could allow students to create separate screens in "Design mode" and then import them into one project.
My understanding is that, at the moment, there isn't a plan to add a collaboration feature like you described. I know it is very technically difficult to do that on the engineering side of things, but I also have heard a lot of teacher requests for this! I totally agree, I think students would LOVE it! It would certainly encourage more collaboration!
Fingers crossed it happens in the future!