The main objective of the present work is to numerically test the performance of a micromechanical model under stress-controlled cyclic loading conditions. This simplified nonincremental model has a peculiarity of taking into account the grain shape effect and introduces an isotropic hardening variable for each slip system. The model shows an ability to predict accommodation, uni- and multiaxial ratchetting phenomena for complex loading paths. The uniaxial ratchetting is more pronounced for relatively higher mean stresses. Moreover, the evolution of intragranular isotropic hardening, mainly in path 1, is found to be dependent on both the sliding nature and the increase of the ACSS number in the case of multiaxial ratchetting. Finally, the main advantage of the explored multiscale approach is in its capability to describe local heterogeneities.