Is it possible to make a symbol map

[BW40]

Is there a way to make a symbol map and manually plot shapes' locations? I need a state map, with county lines and a shape to represent each department in each county (up to five shapes per county). Can BI make a symbol map? Also, preferably there would be a value I could assign to each shape and then filter by the value.

[lbendlin]

Yes, that is what the Shape Map visual does.  You can provide your own polygons in topojson format.  Use Mapshaper.com or equivalent to prepare your data.

[BW40]

Do you happen to have a link to a video or instructions for that? With the shape map I can get a solid colored state but cannot add details. In the ArcGIS maps, I can build a state county map but I cannot not overlay symbols on it (although it is the closest to what I need, if I could just overlap symbols on it), and the icon map gives me a general road map of the state without county lines and it combines my groups rather than letting me create a symbol per county and will not let me actually add shapes. This has been straightforward in other programs but either the capability is hidden for PowerBI or it has not caught up yet. 
Shape map: 

Icon map:

ArcGIS:

[lbendlin]

When you used MapShaper you probably stripped out the polygon attributes. You need those to connect the shapes to your Power BI data.