I would like to make a series of assignments in which my students will produce a short piece of writing, then go back and edit it several times. Is there any way to have students create a google doc that will automatically embed into several different assignments? That way, when they get to the second assignment with the document, their work will already be there for them to add onto.
Currently, I don't think there's a way to connect to the same google doc in multiple assignments automatically. You can search the Ideas space to see if someone has suggested adding similar functionality. If not, you can create a new feature idea to suggest that to Canvas.
The only workaround I can think of (and maybe others can chime in with their thoughts), would be to create a google doc for each student and include that list of google doc links in each assignment with the corresponding student's name. If you did that, though, you'd want to make sure each student only had permission to view their own google doc. If you didn't want to clutter up the details section in each of the assignments, you could list those URLs in a course page and then link to the course page in the assignment details. I hope that all made sense. Let me know if you have questions.