GeoPandas cumulative value sum for intersecting polygons

Question

I have a geojson file for all of the tax areas in the state of Utah. I read it into a GeoPandas dataframe. Now each row represents a tax area polygon.

Many of the tax area polygons overlap each other. For example, a county polygon serves as the foundation layer, and then a city polygon will be placed on top (the county polygon contains city polygons).

Each tax area polygon has a tax rate field. My objective is to add up tax rates where these polygons intersect, so in the end, one could hover over an area, and get the "top most" tax area's name, but have a cumulative sum of the intersecting tax area's rates.

I've looked at:

• Projecting attribute from one polygon layer to another in QGIS?
• Calculating area weighted average of attribute in one layer by shape in another using ArcGIS for Desktop? and
• Finding all polygons overlapping polygons from another layer using MapInfo?

but these use other GIS software, and this is my first time using GeoPandas.

My ultimate goal is to output a new geojson file that has each tax area polygon but with the cumulative rate instead of each individual rate.

Any advice on how to accomplish this?