We use time-series of magma efflux and GPS-derived surface deformation observations to constrain the transfer of compressible magma within the crustal plumbing of the Soufrière Hills volcano for three cycles of effusion and pause. Our system model has two vertically-stacked spherical chambers. Deep melt supply to the system is constrained to be continuous and steady, yielding a rate of 1.2 m3/s, which fixes the geometry of the dual interconnected chambers to depths of about 5 and 19 km. The eruptive volume change of the shallow chamber is in-phase and an order of magnitude smaller than the deep chamber. Significantly, the shallow chamber seems to control the periodic system behavior: surface magma efflux resumes when the shallow chamber reinflates to its initial threshold pre-eruptive volume (triggering re-opening of an eruptive feeder dike), and ceases when it has lost 14–22 Mm3 (106 m3) of its volume (sealing the conduit and staunching magma flow). These observations are consistent with eruption re-initiation and re-cessation controlled by magma overpressure thresholds.