We present inelastic neutron scattering data on the quantum paramagnet AgVOAsO4 that establish the system is a S=1/2 alternating spin chain compound and provide a direct measurement of the spin gap. We also present experimental evidence for two different types of field-induced magnetic order between mu_0H_c1 = 8.4T and mu_0H_c2 = 48.9T, which may be related to Bose-Einstein condensation (BEC) of triplons. Thermodynamic measurements in magnetic fields up to 60T and temperatures down to 0.1K reveal a H-T phase diagram consisting of a dome encapsulating two ordered phases with maximum ordering temperatures of 3.8K and 5.3K respectively. This complex phase diagram is not expected for a single-Q BEC system and therefore establishes AgVOAsO4 as a promising multi-Q BEC candidate capable of hosting exotic vortex phases.
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