I can't be certain I fully understand the context but it sounds like you might want to try Grouping your data instead of creating Sets. If you create a group you can then bring in your original Dimension to the right of the Group you create and see it at two different levels of detail, as a Group or Individually. You could even take it one step further and create a parameter to switch between the group or individual Dimensions. If interested I'd be happy to share steps here to show how to do that if you don't already know.
I hope this helps!