The phase diagram of dense baryonic matter is investigated in the non-relativistic mean-field framework including the full baryonic octet. It is shown that, depending on the thermodynamic conditions, up to three strangeness-driven phase transitions may occur, such that a huge fraction of the total baryonic density domain corresponds to phase coexistence. The phase transitions are associated to the onset of the different hyperonic species or hyperonic families. We demonstrate that, due to a moderate component of the order parameter along the direction of charge density, phase coexistence persists if the Coulomb coupling to the electrons is accounted for. This makes the phase transition potentially relevant for neutron star and supernova evolution. The sensitivity of the results on the hyperonic coupling constants is explored, both for purely phenomenological energy functionals and for functionals adjusted to microscopic BHF calculations. We show that the presence of a phase transition is compatible both with the observational constraint on the maximal neutron star mass, and with the present hypernuclei experimental information. We also show that two solar mass neutron stars are compatible with important hyperon content. Both the $Y$-$N$ channel and the $Y$-$Y$ channel contribute to the phase transition. Still, the parameter space is too large to give a definitive conclusion of the possible occurrence of the phase transition, and further constraints from multiple-hyperon nuclei and/or hyperon diffusion data are needed.