If the same dwg file is referenced twice turning off display of one turns off display of both.
If the file name and logical name are identical, the reference attachments will work as one attachment. ie, turn off the display of one turns off the display of all instances of that file, turn off level display in one turns off that level display in the other attachment.
In the Reference dialog box, double click the attachment. In the Attachment Settings dialog box, change the logical name of one of the attachments. The attachments will now work independent of each other.