Bar plot grouped by serveral criteria?

I have seen examples for how to create a bar plot where one has k bars for each value of a group, e.g. the grouping is by age of person in decades and for each group I have a male and female bar.

But how to generalize this to more (nested) groups.

Staying with a people example: maybe I have gender (2 values), age-decade(e.g. 9 values), employment status (3 values), and yearly income band (5 values) and I want to create a bar chart where I group the bars first by gender (so f/m bars are closest to each other) then by employment status (so I get 3 groups of the 2 gender bars), then yearly income (I get 5 groups, each group has 3 subgroups and each subgroup has 2 bars) and so on. Is this possible?