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If you have only two different Geographic levels (Country and State), you can use a dual axis on the map to plot both.
With Sample Superstore data (which has only US data), I created a "State" field that purposely leaves out some State data, and allowed all the Zip Codes that are in the data set. I did this to ensure we had some States for which there is zip code data but no overall state data.
1. With the "Map" mark type selected, I double-clicked my created State column from the fields list and it auto-generated the map:
2. In the Rows column, CTRL+Click-and-drag the Latitude (generated) pill to duplicate it. Now you have two maps, and both are at the State Level of Detail
3. On the Marks card, leave the first Latitude (generated) level of detail to be State. On the second Latitude (generated) Marks card, remove State as an item of Detail and add PostalCode (drag the PostalCode1 field to the Detail button) as a Level of Detail:
4. Let's overlap the maps. Go to the second Latitude (generated) pill in the Rows Shelf, click the arrow for the drop down box, and choose "Dual Axis".
5. And then format as you like. I would make the State color more transparent, and maybe make the zip code be orange and less transparent:
Hope this helps,
So sorry for the slow reply - really helpful