<p>Cognition is flexible, allowing behavior to change on a moment-by-moment basis. Such flexibility relies on the brain’s ability to route information through different networks of brain regions to perform different cognitive computations. However, the mechanisms that determine which network of regions is active are not well understood. Here, we combined cortex-wide calcium imaging with high-density electrophysiological recordings in eight cortical and subcortical regions of mice to understand the interactions between regions. We found different dimensions within the population activity of each region were functionally connected with different cortex-wide ‘subspace networks’ of regions. These subspace networks were multiplexed; each region was functionally connected with multiple independent, yet overlapping, subspace networks. The subspace network that was active changed from moment-to-moment. These changes were associated with changes in the geometric relationship between the neural response within a region and the subspace dimensions: when neural responses were aligned with (i.e., projected along) a subspace dimension, neural activity was increased in the associated regions. Together, our results suggest that changing the geometry of neural representations within a brain region may allow the brain to flexibly engage different brain-wide networks, thereby supporting cognitive flexibility.</p>