Confidence interval square in a plot with one vari

问题:

Although it might sound easy at first, I do not have a scatterplot. And I think that is what make this question challenging. I am having this plot, which comes from this question.

Summing up, each axis represents a variable that is not connected to the other. It is not an XY scatterplot, as you see.

I wonder to know if there is any possibility to trace the 95% confidence interval for the mean in both variables, and draw a square in the middle of the plot representing the overlapping area among both datasets.

The result might be something similar to this, bearing in mind that 95CL represented do not correspond to reality (just for the sake of illustrating how it might appear):

Here is a another question which deals with this situation, but not using ggplot.