  The problem of finding new metrics of interest, in the context of SUGRA, is
reduced to two stages: first, solving a generalized BPS sigma model with full
quaternionic structure proposed by the authors and, second, constructing the
hyper-K\"{a}hler metric, or suitable deformations of this condition, taking
advantage of the correspondence between the quaternionic left-regular potential
and the hyper-K\"{a}hler metric of the target space. As illustration, new
solutions are obtained using generalized Q-sigma model for Wess-Zumino type
superpotentials. Explicit solutions analog to the Berger's sphere and
Abraham-Townsend type are given and generalizations of 4-dimensional
quaternionic metrics, product of complex ones, are shown and discussed.
