Rank and preference data are becoming increasingly ubiquitous, stimulating continuous advances in preference learning methodologies and their wider adoption across different domains. The Lower-dimensional Bayesian Mallows Models with Mixtures (LowBM3) is a recent extension of the Bayesian Mallows Models, which was originally developed as a unifying Bayesian framework to estimate the Mallows model. LowBM3 extends the Bayesian Mallows Model to ultra-high-dimensional settings, allowing to estimate a clustering of the assessors, and the within-cluster sets of relevant items and their consensus rankings. In this paper, we propose a novel post-processing strategy for LowBM3, named stability post-processing. We validate our methodology through experimental analysis and demonstrate its superior performance in specific settings characterized by significant variability in absolute rankings across assessors.