A new approach has been devised and explored to reconstruct magnetospheric configurations, based on spacecraft data and a synthesis of two methods of modeling the magnetic field of extraterrestrial currents. The main idea is to combine within a single framework (1) a modular structure explicitly representing separate contributions to the total field from the magnetopause, ring, tail, and field-aligned currents, and (2) a system of densely distributed field sources, modeled by the radial basis functions (RBF). In such an arrangement, the modular part takes on a role of the principal component representing the gross large-scale structure of the magnetosphere, whereas the RBF part serves as a higher-order correction that compensates for the lack of flexibility of the modular component. The approach has been tested on four subsets of spacecraft data, corresponding to four phases of a geomagnetic storm, and was shown to tangibly improve the model’s performance. In particular, it allows proper representation of magnetic effects of the field-aligned currents both at low altitudes and in the distant magnetosphere, as well as inclusion of extensive high-latitude field depressions associated with diamagnetism of the polar cusp plasma, missing in earlier empirical models. It also helps to more accurately model the nightside magnetosphere, so that most of the large-scale magnetotail field is compactly described by a dedicated module inherited from an earlier empirical model, while the RBF component’s task is to resolve finer details in the inner magnetosphere.