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Due to the ionosphere's significant impact on radio signal propagation, accurate modeling and reconstructions of its electron density distribution are crucial for various applications involving trans-ionospheric signals, such as GNSS positioning, GNSS augmentation systems (e.g., EGNOS and WAAS), remote sensing, but also to enhance our understanding of ionospheric processes. Several approaches have been developed for ionospheric reconstruction by combination of actual observations with a physical or an empirical background model. When looking for storage space and runtime saving approaches, algebraic iterative methods have been used to ingest current measurements into background models, e.g. derivatives of the Algebraic Reconstruction Technique (e.g. ART, MART) and column-normalized methods (e.g. SART, SMART). Those methods are working without the modification of the model coefficients but by updating the background in the area surrounding the available current measurements.We introduce the new 4D electron density reconstruction approach 4DSMART+ as a combination of SMART, the successive correction method and a time propagation model. We apply 4DSMART+ to reconstruct the electron density distribution within the topside ionosphere and plasmasphere on a global grid with altitudes between 430 and 20200 km for a 59-day period of the year 2015 with moderate ionospheric conditions. STEC measurements of eleven LEO satellites (e.g. Swarm, COSMIC-1, MetOp) are used as data base for the reconstructions where the NeQuick model serves as background.The comparison of the reconstructions to assimilated STEC measurements shows consistency with a median error of 0.1 TECU and a standard deviation of 3.4 TECU. Furthermore, 4DSMART+ is compared to SMART+ and the NeQuick model with respect to its capability to reproduce independent STEC data from the three LEO satellites GRACE and Swarm A. The results show that 4DSMART+ decreases the median STEC error for GRACE and Swarm A STEC by up to ~84% and ~99%, respectively, compared to SMART+ and the NeQuick model. Validation by means of the COSMIC-1 radio occultation profiles shows that 4DSMART+ reduces the median of the relative residuals by up to 13% in comparison to SMART+ and the NeQuick model.