Comet C/2016 R2 (PanSTARRS) has a peculiar volatile composition, with CO being the dominant volatile, as opposed to H2O, and one of the largest N2/CO ratios ever observed in a comet. Using observations obtained with the Spitzer Space Telescope, NASAs Infrared Telescope Facility, the 3.5 m Astrophysical Research Consortium telescope at Apache Point Observatory, the Discovery Channel Telescope at Lowell Observatory, and the Arizona Radio Observatory 10 m Submillimeter Telescope, we quantified the abundances of 12 different species in the coma of R2 PanSTARRS: CO, CO2, H2O, CH4, C2H6, HCN, CH3OH, H2CO, OCS, C2H2, NH3, and N2. We confirm the high abundances of CO and N2 and heavy depletions of H2O, HCN, CH3OH, and H2CO compared to CO reported by previous studies. We provide the first measurements (or most sensitive measurements/constraints) on H2O, CO2, CH4, C2H6, OCS, C2H2, and NH3, all of which are depleted relative to CO by at least 12 orders of magnitude compared to values commonly observed in comets. The observed species also show strong enhancements relative to H2O, and, even when compared to other species like CH4 or CH3OH, most species show deviations from typical comets by at least a factor of 23. The only mixing ratios found to be close to typical are CH3OH/CO2 and CH3OH/CH4. The CO2/CO ratio is within a factor of 2 of those observed for C/1995 O1 (Hale- Bopp) and C/2006 W3 (Christensen) at a similar heliocentric distance, though it is at least an order of magnitude lower than many other comets observed with AKARI. While R2 PanSTARRS was located at a heliocentric distance of 2.8 au at the time of our observations in 2018 January/February, we argue, using sublimation models and comparison to other comets observed at similar heliocentric distance, that this alone cannot account for the peculiar observed composition of this comet and therefore must reflect its intrinsic composition. We discuss possible implications for this clear outlier in compositional studies of comets obtained to date and encourage future dynamical and chemical modeling in order to better understand what the composition of R2 PanSTARRS tells us about the early solar system.