directory rights

 I am setting up directory where I gave domain users list and write so they can move files into a directory and once they are place they cannot delete. However I noticed that they can overwrite an existing file with the same name is there a way to set the rights so they can place a file but not be able to overwrite? I know I can place a deny delete in the advanced for domain users however that would then affect the full access group users and prevent them from deleting since they are members of the domain and full access group.