A challenging problem in bioinformatics is the detection of residues that account for protein function specificity, not only in order to gain deeper insight in the nature of functional specificity but also to guide protein engineering experiments aimed at switching the specificity of an enzyme, regulator or transporter. The majority of the state-of-the art algorithms for this task use multiple sequence alignments (MSA’s) to identify residue positions conserved within- and divergent between- protein subfamilies. In this study, we focus on a recent method based on this approach called multi-RELIEF. We analyze and modify the two core parts of the method in order to improve its predictive performance. A parametric generalization of the popular RELIEF machine learning algorithm for weighting residues is introduced and incorporated in multi-RELIEF. The ensemble criterion of multi-RELIEF for merging the weights of multiple runs is simplified. Finally, the method used by multi-RELIEF for exploiting tertiary structure information is modified by incorporating prior information describing the confidence of the original scores assigned to residues. Extensive computational experiments on six real-life datasets show improvement of both robustness and detection capability of the new multi-RELIEF over the original method.