Resolution:
Designer cannot save non-RCS multi-file project to a VSS system without changing the project directory name,

Possible error:
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If "Save As" option is chosen and value of "Project Directory" field in "Save Project" window is kept the same as existing multi-file project directory, then designer throws error window:

"Already Open

The project with that name is open, you must close it before you can  
save another project with that name. Open project names must be unique  
to resolve project references."

Solution:
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In order to successfully save the existing non-RCS project to a VSS system, one must change the value of "Project Directory" field to a different multi-file project directory.