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The Cosmic Microwave Background (CMB) primordial B-modes signal is predicted to be much lower than the polarized Galactic emission (foregrounds) in any region of the sky pointing to the need for sophisticated component separation methods. Among them, the blind Needlet-ILC (NILC) has great relevance given our current poor knowledge of the B-modes foregrounds. However the expected level of spatial variability of the foreground spectral properties complicates the NILC subtraction of the Galactic contamination. In order to reach the ambitious targets of future CMB experiments, we therefore propose a novel extension of the NILC approach, the Multi-Clustering NILC (MC-NILC), which performs NILC variance minimization on separate regions of the sky (clusters) properly chosen to have similar spectral properties of the B-modes foregrounds emission. Clusters are identified thresholding the ratio of B-modes maps at two separate frequencies which is used as tracer of the spatial distribution of the spectral indices of the Galactic emission in B modes. We consider ratios either of simulated foregrounds-only B modes (ideal case) or of cleaned templates of Galactic emission obtained from realistic simulations. In this work we present an application of MC-NILC to the future LiteBIRD satellite, which targets the observation of both reionization and recombination peaks of the primordial B-modes angular power spectrum with a total error on the tensor-to-scalar ratio $δr < 0.001$. We show that MC-NILC provides a CMB solution with residual foregrounds and noise contamination that is significantly reduced with respect to NILC and lower than the primordial signal targeted by LiteBIRD at all angular scales for the ideal case and at the reionization peak for a realistic ratio. Thus, MC-NILC will represent a powerful method to mitigate B-modes foregrounds for future CMB polarization experiments.