Multiple blend shape weights from a single target mesh

So I've got two meshes, BASE and TARGET.

BASE is a polyCube with 3 subdivisions in the x y and z.
TARGET is BASE duplicated and smoothed using the Sculpt Geometry Tool.

I create a blend shape called ONE by selecting TARGET then BASE and clicking "Create Deformer > Blend Shape"

I select TARGET then BASE and add a new blend shape called TWO to the first blend shape group. 
I now have two blendshapes, ONE and TWO, that do the exact same thing.

If I try to "Paint Blend Shape Weights" it shows the TARGET's mesh name twice, presumably for the two blend shapes.  

Is there a way to paint different blend shape weights for the different blend shapes?