Reconstruction of the magnetic field, electric current, and plasma pressure is provided using a new data mining (DM) method with weighted nearest neighbors (NN) for strong storms with the storm activity index Sym‐H < −300 nT, the Bastille Day event (July 2000), and the 20 November 2003 superstorm. It is shown that the new method significantly reduces the statistical bias of the original NN algorithm toward weaker storms. In the DM approach the magnetic field is reconstructed using a small NN subset of the large historical database, with the subset number KNN ≫ 1 being still much larger than any simultaneous multiprobe observation number. This allows one to fit with observations a very flexible magnetic field model using basis function expansions for equatorial and field‐aligned currents, and at the same time, to keep the model sensitive to storm variability. This also allows one to calculate the plasma pressure by integrating the quasi‐static force balance equation with the isotropic plasma approximation. For strong storms of particular importance becomes the resolution of the eastward current, which prevents the divergence of the pressure integral. It is shown that in spite of the strong reduction of the dominant NN number in the new weighted NN algorithm to capture strong storm features, it is still possible to resolve the eastward current and to retrieve plasma pressure distributions. It is found that the pressure peak for strong storms may be as close as ≈2.1RE to Earth and its value may exceed 300 nPa.