An effective procedure to avoid degeneracies in multidimensional unfolding for preference rank data is proposed. We adopt the strategy of augmenting the data matrix, trying to build a complete dissimilarity matrix, by using copula-based association measures among rankings (individuals), and between rankings and objects (namely, a rank-order representation of the objects through tied rankings). Our proposal is able to both recover the order of the preferences and reproduce the position of both rankings and objects in a geometrical space. Application on real datasets show that our procedure returns non-degenerate unfolding solutions.