Yesterday I purchased the Doomsday Playset. Once again the outfits don't seem to work with other clothing, as the artist advertises.  Is there a work around to filling these gaps?

There is auto-hiding-mesh mechanism on content made by Reallusion or some Featured Developers. The purpose of this mechanism is to fix the possible visual defects/flaws when putting on multiple layer of clothes on a character, which is useful for most cases, but not for all cases.

You can always utilize Mesh Editor to make the mesh show / hide as wanted.
http://manual.reallusion.com/Character_Creator_3/ENU/3/Content/Character_Creator_3/3/08_Creating_Custom_Assets/Showing_Hiding_Meshes_with_Brush.htm

or change the layer of clothing 
http://manual.reallusion.com/Character_Creator_3/ENU/3/Content/Character_Creator_3/3/08_Cloth/Customizing_Clothing_Layers.htm?Highlight=cloth%20layer