With DropBox you can drop a document, or more than one document, into a folder and then share a link to that folder with several people. They will all be able to access that folder, access the documents in there and edit/add as well. I suspect you can do the same thing with OneDrive, I just haven't tried that.
If you also want to share this online I would not publish the link itself, but you can invite people to contact you and share that link through DM or e-mail.