When the same Tag Set exists multiple times in a cell it is only possible to edit the last Tag defined.
Product: MicroStation V8 2004 EditionVersion: 08.05.02.27
There is an ID that connects a tag element to an entry in the tag set definition. So if there are 3 instances of the same Tag Set placed in a cell, they all have the same ID. When you tag the cell multiple times using the same tag set, all the tags float up to be associated to the cell header. Now you have 3 tags that refer to a single entry in the tag definition and MicroStation cannot tell them apart. So only the last tag placed can be modified.