Ideally, this would be implemented in core (taxonomy module). Provide a checkbox on the Taxonomy Manager UI Configuration page that enables or disables the option to create terms with multiple parents.

If this checkbox is not selected the following will occur:
1. When moving terms, the option to "Keep old parents and add new ones (multi-parent). Otherwise old parents get replaced." will not be available.
2. When editing a term, the user can only select one parent.