Estimating the melt fraction and volatile content of regions of partial melt beneath volcanoes has important implications for volcanic hazards since higher melt fraction, volatile-rich magmas are more buoyant and have a lower viscosity, and thus are more susceptible to mobilization and possibly eruption. Magnetotelluric (MT) data can be used to model subsurface bulk resistivity structures through inversion algorithms and can provide information on the distribution and amount of melt and volatiles contained in the residing magma by converting bulk resistivity to estimates of melt fraction, temperature, and water content. These are often treated as independent variables but, in reality, they are thermodynamically correlated. Thermodynamic models such as MELTS can be used to constrain the possible combinations of melt fraction, temperature, and water content such that MT interpretations are petrologically consistent. Probabilistic Bayesian inversion that incorporates these constraints can be used to find a distribution of models and interpretations which fit the MT data and provide a better understanding of the uncertainty in MT-derived estimates of melt fraction. In this study, we apply MELTS-coupled 1-D Bayesian inversions of MT data at Uturuncu Volcano to evaluate the constraints that MT data can provide on melt fraction estimates. Uturuncu Volcano is a large composite volcano in southern Bolivia at the center of the Altiplano Puna Volcanic Complex (APVC), the result of a large ignimbrite flare-up during the past 10 Ma. Previous geophysical studies have shown that the APVC is underlain by the voluminous, laterally-extensive Altiplano Puna Magma Body (APMB) at approximately 15-20 km depth below surface. The APMB has previously been interpreted to have a wide range of melt fractions anywhere from 4% to 45%, but MT results suggest anomalously high water contents of up to 10 wt%. Initial results from petrologically-consistent MT inversion modelling suggests that the resulting low resistivity of the APMB beneath Uturuncu requires high melt fractions (e.g. >90%) in near-saturated conditions. This suggests that either high melt fraction near-saturated magma reservoirs exist at depth or that a significant phase of saline fluids in over-saturated low melt fraction conditions is present.