The Multi-slit Solar Explorer (MUSE) is a proposed mission aimed at understanding the physical mechanisms driving the heating of the solar corona and the eruptions that are at the foundation of space weather. MUSE contains two instruments, a multi-slit EUV spectrograph and a context imager. It will simultaneously obtain EUV spectra (along 37 slits) and context images with the highest resolution in space (0.33-0.4 arcsec) and time (1-4 s) ever achieved for the transition region and corona. The MUSE science investigation will exploit major advances in numerical modeling, and observe at the spatial and temporal scales on which competing models make testable and distinguishable predictions, thereby leading to a breakthrough in our understanding of coronal heating and the drivers of space weather. By obtaining spectra in 4 bright EUV lines (Fe IX 171A, Fe XV 284A, Fe XIX-XXI 108A) covering a wide range of transition region and coronal temperatures along 37 slits simultaneously, MUSE will be able to "freeze" the evolution of the dynamic coronal plasma. We describe MUSE's multi-slit approach and show that the optimization of the design minimizes the impact of spectral lines from neighboring slits, generally allowing line parameters to be accurately determined. We also describe a Spectral Disambiguation Code to resolve multi-slit ambiguity in locations where secondary lines are bright. We use simulations of the corona and eruptions to perform validation tests and show that the multi-slit disambiguation approach allows accurate determination of MUSE observables in locations where significant multi-slit contamination occurs.