gClassFolders is a Google Spreadsheets script that can help you manage the flow of Google Drive files that are shared with you.
gClassFolders is a script that will create folders for you for as many course sections as you need. The concept behind it is this; students have a "dropbox" folder in their Google Drive accounts that you have shared with them. To submit work students drag files into that "dropbox" folder. From there gClassFolders sorts submissions to the correct folder for each student. There are some file naming conventions that you and your students must adhere to, but if you can do that gClassFolders should help you manage shared Google Drive files. You can get detailed set-up directions here from the gClassFolders developer. Watch an overview of the set-up process in the video below.