Parallel Sets is a tool and visualization method for exploring categorical data. Multidimensional data is going to be hard to present without significant design work and hard to interpret for most information seekers. There is a learning curve with these graphs, but once you get used to them they really are very rich and easy to query.
I think the datasets may have stretched the tool a bit. Labels and scaling got a little wonky, but once the data was filtered to a more reasonable set of values along a dimension, brilliant. The order in which the variables are added to the visualization can change the presentation dramatically which really helps in answering different sets of questions.
This could be getting closer to a chart that would be useful for at-a-glance comparisons across collections.