My scenario does not involve minting, but completing the die with a punch.
A well-known case of centrally made dies is France. All dies were made in Paris and shipped out to the provincial mints. These added the mint mark and, if necessary, the mark of the director and chief engraver of the mint. Another example is the UK, where the mint in London outsourced striking some colonial coins to the (private) Birmingham mint. Again, the dies were made in London, the mint marks added locally (or the unwanted mint mark filled in, as the case may be.)
Peter