All ingredients needed exist in some shape or form. I just haven't seen them combined.
I see it as a general table filtering tool.
Parallel Sets recalculated into Parallel Coordinates is a good start. Let's try:
n1, n2, n3, etc., parallel_sets mapped on 0-1 parallel_coordinates
N=sum(n1,n2,n3,..)
stroke-width = 1/N
y= (i-1/2) * (1/N)
Within the set keep the same order as in the neighboring coordinates, or if you have coordinates on both sides, take a sort of average.
If built, it would help many more people from a proper home, therefore I suggested it to GGally: ggobi/ggally#473
JMP software does ParallelCoordinates and ParallelSets chart types combined in one chart
Here you see the chart types coupled, but below each other, interacted with: Parallel coordinates and parallel sets together seems like a great exploratory data analysis tool
To be reproducible (or replayable on a different data set) you need the GUI-actions captured and possible to replay: shinymeta, making GUI-actions reproducible
Now if you could turn your shinyGUI-actions into the more generally used SQL, it would make it awesome power tool. (tidyverse<>SQL things exist, e.g. https://dbplyr.tidyverse.org/articles/translation-verb.html ), would be close to perfect
For material properties: Ashby plots