<p>TOPSIS, a popular method for ranking alternatives, is based on aggregated distances to ideal and anti-ideal points. As such, it was considered to be essentially different from widely popular and acknowledged ’utility-based methods’, which build rankings from weight-averaged utility values. Nonetheless, TOPSIS has recently been shown to be a natural generalization of these ’utility-based methods’ on the grounds that the distances it uses can be decomposed into so-called weight-scaled means (WM) and weight-scaled standard deviations (WSD) of utilities. However, the influence that these two components exert on the final ranking cannot be in any way implemented in the standard TOPSIS. This is why, building on our previous results, in this paper we put forward modifications that make TOPSIS aggregations responsive to WM and WSD, achieving some amount of well interpretable control over how the rankings are influenced by WM and WSD. The modifications constitute a natural generalization of the standard TOPSIS method because, thanks to them, the generalized TOPSIS may turn into the original TOPSIS or, otherwise, following the decision-maker’s preferences, may trade off WM for WSD or WSD for WM. In the latter case, TOPSIS gradually reduces to a regular ’utility-based method’. All in all, we believe that the proposed generalizations constitute an interesting practical tool for influencing the ranking by controlled application of a new form of decision-maker’s preferences.</p>