In our recent paper (Andreeva and Tsyganenko, 2016), a novel method was proposed to model the magnetosphere directly from spacecraft data, with no a priori knowledge nor ad hoc assumptions about the geometry of the magnetic field sources. The idea was to split the field into the toroidal and poloidal parts and then expand each part into a weighted sum of radial basis functions (RBF). In the present work we take the next step forward by having developed a full-fledged model of the near magnetosphere, based on a multiyear set of space magnetometer data (1995–2015) and driven by ground-based and interplanetary input parameters. The model consolidates the largest ever amount of data and has been found to provide the best ever merit parameters, in terms of both the overall RMS residual field and record-high correlation coefficients between the observed and model field components. By experimenting with different combinations of input parameters and their time-averaging intervals, we found the best so far results to be given by the ram pressure Pd, SYM-H, and N-index by Newell et al. (2007). In addition, the IMF By has also been included as a model driver, with a goal to more accurately represent the IMF penetration effects. The model faithfully reproduces both externally and internally induced variations in the global distribution of the geomagnetic field and electric currents. Stronger solar wind driving results in a deepening of the equatorial field depression and a dramatic increase of its dawn-dusk asymmetry. The Earth’s dipole tilt causes a consistent deformation of the magnetotail current sheet and a significant north-south asymmetry of the polar cusp depressions on the dayside. Next steps to further develop the new approach are also discussed.