The investigation of almost paracontact almost paracomplex manifolds is further developed. These manifolds, referred to briefly as Π-manifolds, are equipped with a pair of mutually related compatible metrics: a Riemannian metric and a pseudo-Riemannian metric. Based on the established classification with respect to the Riemannian metric and the corresponding alternative classification with respect to the associated pseudo-Riemannian metric, two examples on a tree-dimensional Lie group are presented to illustrate the most significant case of the transition between the two classifications.