S U M M A R Y Measurements of the spatio-temporal variations of Earth's gravity field from the Gravity Recovery and Climate Experiment (GRACE) mission have led to new insights into large spatial mass redistribution at secular, seasonal and subseasonal timescales. GRACE solutions from various processing centres, while adopting different processing strategies, result in rather coherent estimates. However, these solutions also exhibit random as well as systematic errors, with specific spatial patterns in the latter. In order to dampen the noise and enhance the geophysical signals in the GRACE data, we propose an approach based on a data-driven spatio-temporal filter, namely the Multi-channel Singular Spectrum Analysis (M-SSA). M-SSA is a data-adaptive, multivariate, and non-parametric method that simultaneously exploits the spatial and temporal correlations of geophysical fields to extract common modes of variability. We perform an M-SSA analysis on 13 yr of GRACE spherical harmonics solutions from five different processing centres in a simultaneous setup. We show that the method allows us to extract common modes of variability between solutions, while removing solution-specific spatio-temporal errors that arise from the processing strategies. In particular, the method efficiently filters out the spurious north-south stripes, which are caused in all likelihood by aliasing, due to the imperfect geophysical correction models and low-frequency noise in measurements. Comparison of the M-SSA GRACE solution with mass concentration (mascons) solutions shows that, while the former remains noisier, it does retrieve geophysical signals masked by the mascons regularization procedure.