You must create copies of the county layer, and use a different field from the join table for the symbology of each copy. First, load the county layer using the Add Data button. Then join the table to this county file, either by right clicking on the layer and selecting ‘Joins and relates’ or opening Layer Properties and selecting the Joins & Relates tab.

This will be your base or starting file. Right click on the layer, and click Copy. Then go up to the top of the list of layer to the Data Frame name and right click on Paste Layer. This will create a new copy of the county layer. Open the Layer Properties for this newly added layer, and change the symbology using the first field from the join table. Under the General tab (still in Layer Properties) also change the Layer Name from ‘county’ to something more descriptive.

Go back to the Data Frame name, right click and choose ‘Paste Layer’ again. ArcMap will remember the layer from the previous Copy/Paste and paste the county layer again.

Continue to change the field used and the Layer Name as needed.