I take a more extreme view compared to many here: One should avoid stack bar charts at all costs and double stacked bar charts sounds like real bad dream. Not making double stacked bar charts easy to do I'm sure is not by design but I'm glad it's hard to do.

I believe that the incentive to have stacked bar charts is to attempt to display several aspects of the data in a single figure. But usually the resulting display does not convey any of the multiple aspects very well. Unless you have some limitation on pages, one should have separate figures for each objective. Maybe in the olden days where things were printed, there was the need to cut down on the number of figures. But not any more.

Do a Google search for "alternatives to stacked bar charts" and you'll see alternatives and why stacked bar charts (and bar charts for that matter) have undesirable properties.

But how can you have double stacked chartbars? For example, how can you show supply and demand for multiple locations? How can you show, for different regions, the supply and demand of water (e.g. on one side runoff and infiltration and on the other side use in agriculture, use in industry, use for public water supply)?