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. We focus herein on two different improvements of the aforementioned approach: (i) we study the behavior of the method for classical nonlinearities involved in poroelasticity problems and (ii) to improve modularity of the partitioning we propose a multi-space-scale appoach to deal with independent meshes for each physics.