If you go to the Admin window and right click on File Types it shows you the options for duplicate file names and it doesn't look like what you are looking for is an option. Do your drawings have to have the same name exactly? Otherwise you could always have an A1010-01 and A1010-02 or something similar. This way they would have the same family name but the suffix would indicate which drawing type it would be.
By same directory do you mean the same folder? If so no. On this same note I have been told by SolidWorks, duplicate files may cause performance issues with EPDM. I think Stephen's suggestion is the correct way to go even if you could have the same file name in the same folder.
That's what we were afraid of over here. And yes, that is what I meant (weather it be a folder or the root)