To get different slices of the pie, you'll have to slice the data with discrete values (such as the Product dimension) and you should have one or more values for each Lat/Lon. Since Lat/Lon is defined by city in your screenshot, you'll want to use something else other than city to slice the pie so that you get more than one pie slice at each location.
I've attached your workbook here to demonstrate some possibilities. Note that I copied the Latitude field on the Rows shelf (CTL + drag the field) to get a dual axis map. That let me have a filled map with pies on top. You'll definitely want to play with it to get it to look the way you want.
Pie chart on Filled map.twbx.zip 212.1 KB