Help Understanding results of Offset Paths in Illustrator

I created this star with another shape inside it along with the and R which was converted to outlines. I knocked out the center shape  of the star with the Shape Builder.

I selected each shape and added a small "offset path" which gave me the images on the right.

If I wanted to add one more outline, but only to the outer outline, how do I do that. When I select the outer path, selected both new outlines. If I did the Offset Path command, it outlines outside the outer one and another on the inside of the smaller one. 

This is just a simple example, but I might need to add an outline around a graphic with dozens of elements. 

Do I have to find the sub-layer of the outlines to be able to isolate it to outline it?