The interactions among brain entities, commonly computed through pair-wise functional connectivity, are assumed to be manifestations of information processing which drive function. However, this focus on large-scale networks and their pair-wise temporal interactions is likely missing important information contained within fMRI data. We propose leveraging multi-connected features at both the voxel- and network-level to capture 'multi-way entanglement' between networks and voxels, providing improved resolution of interconnected brain functional hierarchy. Entanglement refers to each brain network being heavily enmeshed with the activity of other networks. Under our multi-connectivity assumption, elements of a system simultaneously communicate and interact with each other through multiple pathways. As such we move beyond the typical pair-wise temporal partial or full correlation. We propose a framework to estimate functional multi-connectivity (FMC) by computing the relationship between system-wide connections of intrinsic connectivity networks (ICNs). Results show that FMC obtains information which is different from standard pair-wise analyses.