The Multiply blend mode can only darken a layer, not brighten it, so you could only use it for adding shadows from a hillshade layer to a base map, but not the highlights.
I would use the "Overlay" blend mode for this, rather than "Multiply". With Overlay, areas where the top layer is brighter than the bottom layer are brightened, and ...
After chatting with folks on the Spatial Community slack channel, we were able to generate a nice plot. I had to set the crs parameter in the .add_basemap() function.
ax = unknown_transfer_loc.plot(figsize=(12,7))
cx.add_basemap(ax, zoom=15, crs='EPSG:4326', source=cx.providers.CartoDB.Voyager)