Doping a semiconductor with foreign atoms enables the control of its electrical and optical properties. We transplant the concept of doping to macroscopic photonics, demonstrating that two-dimensional dielectric particles immersed in a two-dimensional epsilon-near-zero medium act as dopants that modify the medium’s effective permeability while keeping its effective permittivity near zero, independently of their positions within the host. The response of a large body can be tuned with a single impurity, including cases such as engineering perfect magnetic conductor and epsilon-and-mu-near-zero media with nonmagnetic constituents. This effect is experimentally demonstrated at microwave frequencies via the observation of geometry-independent tunneling. This methodology might provide a new pathway for engineering electromagnetic metamaterials and reconfigurable optical systems.