How to have students working together share and combine code?

I’m trying to have students collaborate to create a multi-screen app, but is there a way for them to work on code simultaneously? Ideally, it would be a google docs style collab but anything would do.

No. They would have to share and remix code. And then copy paste it all together. There is no straightforward way to do it as in Google docs. You could write to support@code.org and request this feature.