Finer control over visuals interaction?

Hello,

I am trying to have three visuals interact as if they were drilled-down from to the other, for lack of better explanation.

Donut chart1 is filtering donut chart2 when one item is selected.

Donut chart2 is filtering donut chart3 when an item is selected in chart2.

I have used the "Edit interactions" accordingly however it does no seems to be possible to achieve the result I am seeking.

Chart 1 will indeed filter chart 2 correctly. but I when I selected one category in chart 2, chart 1 filter is reset, chart 2 is showing all values like it was prior to making a selection in chart 1. Same behavior between chart 3 and chart 2.

An image is more explicit, here are the pages at the various stage of interaction:

Initial page display, all sites in left side. All categories and subcategories on the right-side:

A site is selected; accordingly, only the category manufactured at this site are displayed in the second chart, really neat!

Here is where the dream collapse... making a selection in the second chart to view only the related subcategory actually reload all category as the site is "unselected". The related subcategory are displayed but since the site chart is reset, the numbers are not good, they are global values, not the site's value. The interaction between chart2 and chart1 is set to "No interaction"; same thing for chart3 towards chart1 (and chart2 for that matter):

Can I reproduce the equivalent of a drill-down with a single chart but spread visually on separare visuals?

Regards