In order to increase the reachable workspace of parallel robots, a promising solution consists of the definition of optimal trajectories that ensure the non-degeneracy of the dynamic model in the Type 2 (or parallel) singularity and allow to cross it. However, this assumes that the control law can perfectly track the desired trajectory, which is impossible due to modeling errors. This paper improves the results obtained previously by two of the authors of the present work that defined a robust multi-model approach allowing parallel robots to cross Type 2 singularities. The main idea was to shift near singularities the general dynamic model to a simplified one that can never degenerate. However, because in Type 2 singularity, the robot is locally overconstrained, we will show that the simplified dynamic model admits infinity of exact solutions. We propose to use the solution leading to a null overconstraint in order to avoid undesirable effects near singularities, such as buckling or unstability. The mentioned multi-model control approach is modified accordingly and it is then applied on a prototype of five-bar mechanism to show the effects of correctly and not-correctly managed overconstraint.