A new empirical magnetic field model is being developed, based on a recently proposed radial basis functions (RBF) approach and a multi-year set of spacecraft data by Cluster, Themis, Polar, and Van Allen Space Probes missions, covering quiet and storm time intervals between 1996 and 2016. In terms of the disturbance level, the model's validity range extends to moderate storms with peak SYM-H values down to -150 nT. The study is focused on the inner magnetospheric domain with mostly closed magnetic field lines. The magnetic field is represented as a vector
function of coordinates, dipole tilt angle, solar wind ram pressure, interplanetary magnetic field (IMF), and a set of dynamic variables, quantifying the magnetospheric response to the external driving/loading during the storm active phase, followed by its internal relaxation/dissipation during the recovery phase. The model explicitly describes the IMF By 'penetration' into the near/inner magnetosphere and the resulting behavior of the conjugate footpoints of geomagnetic field lines.