We can use GeoServer to use map tiles from an external service. There are many compatible services:

• Which external services are compatible with GeoServer?

How can we use multiple layers, possibly loaded from multiple different servers, in a way that integrates well with the GeoGraphics functionality and also work with DynamicGeoGraphics?

For example, using the definitions from the above linked answer,

base = GeoGraphics[{Entity["Country", "Hungary"]}, 
  GeoServer -> stamen["watercolor"]]

labels = GeoGraphics[{Entity["Country", "Hungary"]}, 
  GeoServer -> carto["light_only_labels"]]

We could layer these together manually using one of multiple possible ways, e.g.

Overlay[{base, labels}]

But this is not a good solution because it requires multiple GeoGraphics calls that are independent, and does not work with functions like DynamicGeoGraphics.

We can use GeoServer to use map tiles from an external service. There are many compatible services:

• Which external services are compatible with GeoServer?

These services often provide unlabelled background maps, as well as various layers to superimpose on a base map (e.g. labels only, borders only, etc.).

How can we use multiple layers, possibly loaded from multiple different servers, in a way that integrates well with the GeoGraphics functionality and also work with DynamicGeoGraphics?

For example, using the definitions from the above linked answer,

base = GeoGraphics[{Entity["Country", "Hungary"]}, 
  GeoServer -> stamen["watercolor"]]

labels = GeoGraphics[{Entity["Country", "Hungary"]}, 
  GeoServer -> carto["light_only_labels"]]

We could layer these together manually using one of multiple possible ways, e.g.

Overlay[{base, labels}]

But this is not a good solution because it requires multiple GeoGraphics calls that are independent, and does not work with functions like DynamicGeoGraphics.