We presented empirical reconstructions of the magnetic field, electric currents, and force-balanced plasma pressure distributions for two strong storms, the March 2015 and July 2000 events. This included high spatial resolution and high selectivity of the model, which uses only about 0.3% of more than 2 million historical magnetometer records to build a snapshot of the magnetosphere at the moment of interest. The latest version of the new generation empirical models TS07D was used for the reconstruction with 260 basis functions for equatorial currents, flexible field aligned current distributions reproducing the spiral structure of low-altitude current distributions, and the nowcasting binning functions that allow one to use only past information on the global state of the magnetosphere and its solar wind input to build the model. We compared the modeling results with in situ observations of the plasma pressure made with the help of the VA Probe B and with ENA emissions of the storm time plasma showing its pressure distributions and available for both events due to TWINS and IMAGE missions. Our pressure reconstruction became possible due to the resolution of the innermost eastward current whose contribution limits the pressure integral (5) and determines the location and amplitude of the pressure peak. It is shown that a combination of the statistical analysis of the model bins and direct ENA observations of the pressure spatial structure may give realistic pictures of the storm time pressure distributions even for strong storm events. These distributions can then be used to improve the first-principles modeling of these extreme events, and in particular, to adjust the equation of state in global MHD models of the magnetosphere.