Usually, multiphysics phenomena and coupled-field problems lead to computationally intensive structural analysis. Strategies to keep these problems computationally affordable are of special interest. For coupled fluid-structure problems, for instance, partitioned procedures and staggered algorithms are often preferred to direct analysis. In a previous paper, a new strategy derived from the LArge Time INcrement (LATIN) method was described. This strategy was applied to the consolidation of saturated porous soils, which is a highly coupled fluid-solid problem. The feasibility of the method and the comparison of its performance with that of a standard partitioning scheme (the so-called ISPP method) was presented. Here, we go one step further and use the LATIN method to take into account the different time scales which usually arise from the different physics. We propose a multi-time-scale strategy which improves the existing method.