Copy items from another object into all existing cases

I need to update all existing cases with required items (with multiple properties) that have been added to another object. I tried to do this with a new rule and copy the required items in all existing cases, but in the fields where I need to specify where the values should be copied from, the one-to-many relationship is not listed.
Any ideas on how to do this?

I think you will just need to just do this in the reverse direction. I.e. fire a rule on each existing case (using a signal for example), to copy the values in from the source location.