This is not implicitly possible using the qlik map yet, but there is a work around to achieve this. Its a long process and needs to be built as an extension.
1) Gather the polygon information for all the states and cities you need to drill down into.
2) create a hierarchy with the state polygon information and city polygon information. This will be a drill down dimension,
3) Now you will have to create an extension (Preferably using D3) and fetch the data using the hypercube generated by the drill down dimension you created, the polygon information and measure.
4) Hypercube is recreated everytime you make a selection, the extension will only be taking the relevant polygon information
5) In the paint function use D3 to draw an SVG using this polygon information.
6) If needed you can have more functionalities added in like conditional colouring, tooltips, legends etc
I've seen that you posted a couple of questions related to GeoQlik for Qlik Sense.
May I suggest that you contact us directly at firstname.lastname@example.org?
We will be happy answer any question and assist you with your GeoQlik implementation / testing.