I'm not sure if there are any easy ways of doing this when using the simple box plot graph element.
But you can overlay it with bar chart (float) and get something like this IF you can change width proportion of box plot
You can go a bit further using 2 bar charts, one to hide the black line of box plot (I used white color) and then other to display the line. Note that you might have to change the order of these elements and you might have to adjust the width proportion
@scwise , any other ideas how to modify part of box plot (median line)?
-Jarmo