I have a table of data with start and end dates
I want to report this to show the number that were live at the end of each month

I can do this with some dynamic array formulae, but I want to display/filter/total this by various criteria, with all the functionality that pivot tables bring (like incorporating extra departments, or a new column for Full/Part Time)
Can this be done with a pivot table?

Illustrative spreadsheet attached

Thanks

jim