We analyze the multilayer architecture of the global input-output network using sectoral trade data (WIOD, 2016 release). With a focus on the mesoscale structure and related properties, our multilayer analysis takes into consideration the splitting into industry-based layers in order to catch more peculiar relationships between countries that cannot be detected from the analysis of the single-layer aggregated network. We can identify several large international communities in which some countries trade more intensively in some specific layers. However, interestingly, our results show that these clusters can restructure and evolve over time. In general, not only their internal composition changes, but the centrality rankings of the members inside are also reordered, industries from some countries diminishing their role and others from other countries growing importance. These changes in the large international clusters may reflect the outcomes and the dynamics of cooperation, partner selection and competition among industries and among countries in the global input-output network.