In a computerized method and magnetic resonance (MR) system for the supplementation of acquired MR data, at least one supplemented MR data set is determined from multiple acquired, reduced MR data sets that can be acquired with an accelerated acquisition method (such as partially parallel acquisition method, ppa) in which k-space is undersampled. The acquisition can thereby take place in parallel with multiple acquisition coils. In the method and system, a reconstruction kernel is applied to the multiple acquired, reduced MR data sets in order to determine a reconstructed MR data set for an acquisition coil. The reduced MR data set acquired with the acquisition coil is reused in this reconstructed MR data set. The reuse takes place by a combination with weighting with the respective variances.