Biomicrofluidic systems that can recapitulate complex biological processes with precisely controlled 3D geometries are a significant advancement from traditional 2D cultures. To this point, these systems have largely been limited to either laterally adjacent channels in a single plane or vertically stacked single-channel arrangements. As a result, lateral (or transverse) and vertical (or normal) diffusion have been isolated to their respective designs only, thus limiting potential access to nutrients and 3D communication that typifies in vivo microenvironments. Here we report a novel device architecture called "TANDEM", an acronym for "T̲ransverse A̲nd N̲ormal D̲iffusional E̲nvironments for M̲ultidirectional Signaling", which enables multiplanar arrangements of aligned channels where normal and transverse diffusion occur in tandem to facilitate multidirectional communication. We developed a computational transport model in COMSOL and tested diffusion and culture viability in one specific TANDEM configuration, and found that TANDEM systems demonstrated enhanced diffusion in comparison to single-plane counterparts. This resulted in improved viability of hydrogel-embedded cells, which typically suffer from a lack of sufficient nutrient access during long-term culture. Finally, we showed that TANDEM designs can be expanded to more complex alternative configurations depending on the needs of the end-user. Based on these findings, TANDEM designs can utilize multidirectional enhanced diffusion to improve long-term viability and ultimately facilitate more robust and more biomimetic microfluidic systems with increasingly more complex geometric layouts.