1 The aim of data mining is to find novel and actionable insights. However, most algorithms typically just find a single explanation of the data even though alternatives could exist. In this work, we explore a general purpose approach to find an alternative clustering of the data with the aid of mustlink and cannot-link constraints. This problem has received little attention in the literature and since our approach can be incorporated into many clustering algorithm that uses a distance function, compares favorably with existing work.