What do you mean by selecting a project to save a new part?
In epdm Data base server shows to every user an image of all folders an files from a vault. When a user get a version of any file from vault the project folder, where this file reside, is created also on his workstation.
So, you must understand the project folder as an usual local folder and you can create any numbers o files. Those files reside only on your workstation till first checkin. On checkin epdm creates a copy of the file on archive server (version 1).
If you set condition for "Do not allow duplicate for this file extension", and file already exists in vault, epdm warns you about it.