Mount Cleveland is one of Alaska's most active volcanoes, yet little is known about the magmatic system driving persistent and dynamic volcanic activity. Volcanic gas and melt inclusion (MI) data from 2016 were combined to investigate shallow magmatic processes. SO2 emission rates were between 166 and 324 t/day and the H2O/SO2 was 600 ± 53, whereas CO2 and H2S were below detection. Olivine‐, clinopyroxene‐, and plagioclase‐hosted MIs have up to 3.8 wt.% H2O, 514 ppm CO2, and 2,320 ppm S. Equilibration depths, based on MI H2O contents, suggest that a magmatic column extended from 0.5 to 3.0 km (~10–60 MPa). We used MI data to empirically model open‐system H‐C‐S degassing from 0 to 12 km and found that a column of magma between 0.5 and 3 km could produce the measured gas H2O/SO2 ratio. However, additional magma deeper than 3 km is required to sustain emissions over periods greater than days to weeks, if the observed vent dimension is a valid proxy for the conduit. Assuming an initial S content of 2,320 ppm, the total magma supply needed to sustain the annual SO2 flux was 5 to 9.8 Mm3/yr, suggesting a maximum intrusive‐to‐extrusive ratio of 13:1. The model predicts degassing of <50 t/day CO2 for July 2016, which corresponds to a maximum predicted CO2/SO2 of 0.2. Ultimately, frequent recharge from deeper, less degassed magma is required to drive the continuous activity observed over multiple years. During periods of recharge we would expect lower H2O/SO2 and measurable volcanic CO2.