Although cascading failures caused by overload on interdependent/interconnected networks have been studied in the recent years, the effect of overlapping links (inter-similarity) on robustness to such cascades in coupled networks is not well understood. This is an important issue since shared links exist in many real-world coupled networks. In this paper, we propose a new model for load-based cascading failures in multiplex networks. We leverage it to compare different network structures, coupling schemes, and overload rules. More importantly, we systematically investigate the impact of inter-similarity on the robustness of the whole system under an initial intentional attack. Surprisingly, we find that inter-similarity can have a negative impact on robustness to overload cascades. To the best of our knowledge, we are the first to report the competition between the positive and the negative impacts of overlapping links on the robustness of coupled networks. These results provide useful suggestions for designing robust coupled traffic systems.