Maps with Multiple Heat Maps and Other Data

We're about to embark on a small project that requires us to plot various data on a map. Some examples that we need to put on the map:

  1. Population
  2. Income
  3. House Prices
  4. Crime
  5. Etc

Examples 1-3 could be individually plotted using a heat map. However, what if we wanted to show all 3 data simultaneously? We can't have a heat map on top of a heat map, can we?

And what about plotting something like crime? That's not something that would work well as a heat map, right? Crime might be classified as "petty crime" and "violent crime" for a given location. We don't think of those classification as a graduation that can be put in a heat map.

Any suggestions (or examples) on how to effectively display complex data on a map?