Cognition is flexible. Behaviors can change on a moment-by-moment basis. Such flexibility is thought to rely on the brain’s ability to route information through different networks of brain regions in order to support different cognitive computations. However, the mechanisms that determine which network of brain regions is engaged are unknown. To address this, we combined cortex-wide calcium imaging with high-density electrophysiological recordings in eight cortical and subcortical regions of mice. Different dimensions within the population activity of each brain region were functionally connected with different cortex-wide ‘subspace networks’ of regions. These subspace networks were multiplexed, allowing a brain region to simultaneously interact with multiple independent, yet overlapping, networks. Alignment of neural activity within a region to a specific subspace network dimension predicted how neural activity propagated between regions. Thus, changing the geometry of the neural representation within a brain region could be a mechanism to selectively engage different brain-wide networks to support cognitive flexibility.