We study the totally asymmetric simple exclusion process on multiplex networks, which consist of a fixed set of vertices (junctions) connected by different types of links (segments). In particular, we assume that there are two types of segments corresponding to two different values of hopping rate of particles (larger hopping rate indicates particles move with higher speed on the segments). By simple mean-field analysis and extensive simulations, we find that, at the intermediate values of particle density, the global current (a quantity that is related to the number of hops per unit time) drops and then rises slightly as the fraction of low-speed segments increases. The rise in the global current is a counterintuitive phenomenon that cannot be observed in high or low particle density regions. The reason lies in the bimodal distribution of segment densities, which is caused by the high-speed segments.