Onsager's Reciprocal Relations between thermodynamic forces and fluxes, for which Onsager was awarded the Nobel Prize, automatically follow from Thermodynamic Extremal Principles. Thus, the principles have been up to now non-applicable for the treatment of experimentally determined or theoretically modeled non-reciprocal systems as e.g. those involving magnetic fields. Recently, we were able to demonstrate that adding of a certain barrier constraint as bilinear form of thermodynamic forces and fluxes accounted by the Thermodynamic Extremal Principles leads to non-reciprocal relations between the thermodynamic forces and fluxes. In this work, we extend this formulation to rate-independent systems possessing non-differentiable dissipation functions. As an application, we show that the non-associated models of pressure dependent plasticity can be obtained in this fashion.