Muon imaging has recently emerged as a powerful method to complement standard geophysical tools in the study of the Earth’s subsurface. Muon measurements yield a radiography of the average density along the muon path, allowing to image large volumes of a geological body from a single observation point. Long-term measurements allow to infer density changes by tracking the associated variations in the muon flux. In the context of volcanic hydrothermal systems, this approach helps to characterize zones of steam formation, condensation, water infiltration and storage. We present results of imaging the La Soufrière de Guadeloupe dome and shallow active hydrothermal system with a network of muon telescopes viewing the dome from different positions around its base. First, we jointly invert the muon radiographies of the different telescopes with gravity data to obtain a three-dimensional density model of the lava dome. The model reveals an extended low density region where the hydrothermal system is most active. We then analyze the dynamics of the hydrothermal system from long-term measurements (more than 2 years of almost non-interrupted acquisition) with 5 simultaneous muon telescopes. We identify a periodicity of ~1-2 months in the density increase/decrease in the most active zones below fumaroles and acid boiling ponds. Our simultaneous-muon telescope strategy provides constraints on the three-dimensional location of the density changes and an improved quantification of the associated mass flux changes. We compare the temporal trends acquired by the different muon telescopes to time-series of rainfall on the summit recharge area as well as to ground temperature profiles in the vicinity of thermal anomalies and high-discharge summit fumaroles.