How to create a faceting based on a column in second dataframe

Question

I want to create a graph that looks like:

Now I found the cowplot package which gave me a quite similar result.

library(ggplot2)
library(cowplot)
library(data.table)
library(ggridges)

d = data.table(iris)

a = ggplot(data = d, aes(x=Sepal.Length, y=..count..)) +
  geom_density_line() + 
  geom_density_line(data = d[Species == "virginica"], aes(), fill="lightblue", color="darkblue") +
  theme_bw()

b = ggplot(data = d, aes(x=Sepal.Length, y=..count..)) +
  geom_density_line() + 
  geom_density_line(data = d[Species == "versicolor"], aes(), fill="lightgreen", color="darkgreen") +
  theme_bw()

cowplot::plot_grid(a, b, labels=NULL)

The result looks like:

But, there are two points that bother me:

• It has a y-axix in both plots
• With my real data where I have up to 10 grids, the code becomes very long

I think it must be possible to use facet_grid(), facet_wrap() or something similar to achieve this. But I don't know how I can use a column from the dataframe of the second geometry to create these subsets without changing/losing the greyish background plot.