Fluorescence Resonance Energy Transfer (FRET) microscopy has emerged as a powerful tool to visualize nanoscale protein-protein interactions while capturing their microscale organization and millisecond dynamics. Recently, FRET microscopy was extended to imaging of multiple donor-acceptor pairs, thereby enabling visualization of multiple biochemical events within a single living cell. These methods require numerous equations that must be defined on a case-by-case basis. Here, we present a universal multispectral microscopy method (N-Way FRET) to enable quantitative imaging for any number of interacting and non-interacting FRET pairs. This approach redefines linear unmixing to incorporate the excitation and emission couplings created by FRET, which cannot be accounted for in conventional linear unmixing. Experiments on a three-fluorophore system using blue, yellow and red fluorescent proteins validate the method in living cells. In addition, we propose a simple linear algebra scheme for error propagation from input data to estimate the uncertainty in the computed FRET images. We demonstrate the strength of this approach by monitoring the oligomerization of three FP-tagged HIV Gag proteins whose tight association in the viral capsid is readily observed. Replacement of one FP-Gag molecule with a lipid raft-targeted FP allowed direct observation of Gag oligomerization with no association between FP-Gag and raft-targeted FP. The N-Way FRET method provides a new toolbox for capturing multiple molecular processes with high spatial and temporal resolution in living cells.