One not yet mentioned but valid according to certain interpretations of the question... Chinley to Navigation Road. There is a direct line between them but part of it is freight-only. Would it make a useful service to anyone? Yes, there is a known traffic flow between North Wales/Chester/Mid Cheshire and Sheffield and beyond, so this service if it existed would allow those journeys to be done by a shorter route avoiding Manchester or Stockport.
Whilst I think of it, isn't Chinley and Hazel Grove another example now that the 1725 Piccadilly-Chinley via Hazel Grove has stopped running? And that is not a freight line.