Improved external chargers for charging an implantable medical device, and particularly useful in charging a plurality of such devices, are disclosed. Each of the various embodiments include a plurality of field customization coils for customizing the magnetic charging field generated by the external charger such that the magnetic charging field is not radially symmetric. For example, one embodiment includes a primary coil with a plurality of field customization coils distributed radially with respect to the coil. The generated magnetic charging field can be rendered radially asymmetric by selectively activating or disabling the field customization coils in response to data quantifying the coupling between the various implants and the field customization coils in the charger. If there is a relatively high coupling between a particular implant and a particular customization coil for example, that customization coil can be activated to counter the magnetic charging field at that location, while still maintaining a relatively high magnetic charging field at the location of other implants that may have lower couplings.