1. Open your STB based drawing, unlock all layers, use COPYBASE (or COPYCLIP) command to copy All objects to clipboard, create new drawing from CTB based template (acad.dwt, acadiso.dwt, etc.), paste clipboard contents to it. Now your drawing become CTB based. But you will lose drawing depended settings (LTSCALE, unused Layers, TEXT and DIM Styles, etc.)
2. Another way, that will retain everything in drawing, but this way little bit harder:
Open your STB based drawing, save it as 2013 DXF. Close DXF file (answer No to "Save in AutoCAD 2013 Drawing format ?" question).
You will get huge text file, that you can open and save in any text editor, that allows to save PLAIN text without formatting (I use TextWrangler from App Store, but I think that TextEdit will do the work too).
After you open DXF file in preferred text editor, use Find function to find "$PSTYLEMODE" string, this will bring you to these strings in DXF file:
$PSTYLEMODE 290 0 9
substitute 0 for 1:
$PSTYLEMODE 290 1 9
Save file. Open DXF file in AutoCAD and save it as DWG. Your DWG became CTB based.