Multiphysics phenomena lead to computationally intensive structural analyses. Recently, a new strategy derived from the LATIN method was described and successfully applied to the consolidation of saturated porous soils. One of the main achievements was the use of the LATIN method to take into account the different time scales which usually arise from the different physics: a multi-time-scale strategy was proposed. Here we go one step further and use the LATIN method to deal with some of the classical nonlinearities of poroelasticity problems (such as non-constant stiffness and permeability) and we show that these phenomena do not result in a significant increase of the computation cost.