I know that the best way to customise a theme is to make a child theme. In this instance I am helping someone make changes to an existing 3rd party child theme, can I make a child theme of a child theme?
No, for better or worse WordPress only support single level of theme inheritance. You would need to either apply modifications without modifying it via hooks (if possible at all) or fork it.
If specific child theme receives updates be careful to disable them - explicitly by excluding from update checks or implicitly by changing its information details. Otherwise update will wipe out customization.