Out of the box it's not possible to save a WTPart with their documents to a new number.
The Save As collector for WTDocuments is not available in the wizard. Please add this possibility to create a complete copy of a document with the part and revise. Also add the action to the WTDocument to save this document to a new number. At the moment it's only possible if you copy the WTDocument and paste it in a folder. Then a copy will be created. The behavior should be the same as to the CAD-Document.