Here's a comprehensive example using setfacl which gives you that granular control you requested on a per-directory basis where new files will be created with the write attribute for the group:
1.Create the group that will own the shared folder:
sudo addgroup projects
2.Create the folder "project1" we want to share in an appropriate FHS path such as /srv:
sudo mkdir /srv/project1
3.Change ownership of the shared folder "project1" to group "projects":
sudo chown root:projects /srv/project1
4.Set the mode on the folder to be be writable to group members, but only allow the owner to delete their own files:
sudo chmod -R 1775 /srv/project1
4.Add your users to the group "projects":
sudo usermod -a -G projects user1
sudo usermod -a -G projects user2
5.Users must log-out and log back in to recognize the new group memberships
6.Finally, apply setfacl so all new files are created writable by group members:
sudo setfacl -d -m group:projects:rwx /srv/project1
Users can now edit each other's files. In terms of managing group documents, a versioning system such as Git is going to be a better solution