We analyse 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, we find that the multilayer analysis that takes into consideration the splitting into industry-based layers is able 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, with the diminishing role of industries from some countries and the growing importance of those from some other countries. These changes in the large international clusters may reflect the outcomes and the dynamics of cooperation as well as competition among industries and among countries in the global input-output network.