We report the detection of a new planetary system orbiting the nearby M2.5V star GJ357, using precision radial-velocities from three separate echelle spectrographs, HARPS, HiRES, and UVES. Three small planets have been confirmed in the system, with periods of 9.125+/-0.001, 3.9306+/-0.0003, and 55.70+/-0.05 days, and minimum masses of 3.33+/-0.48, 2.09+/-0.32, and 6.72+/-0.94 Me, respectively. The second planet in our system, GJ357c, was recently shown to transit by the Transiting Exoplanet Survey Satellite (TESS; Luque et al. 2019), but we could find no transit signatures for the other two planets. Dynamical analysis reveals the system is likely to be close to coplanar, is stable on Myrs timescales, and places strong upper limits on the masses of the two non-transiting planets b and d of 4.25 and 11.20 Me, respectively. Therefore, we confirm the system contains at least two super-Earths, and either a third super-Earth or mini-Neptune planet. GJ357b & c are found to be close to a 7:3 mean motion resonance, however no libration of the orbital parameters was found in our simulations. Analysis of the photometric lightcurve of the star from the TESS, when combined with our radial-velocities, reveal GJ357c has an absolute mass, radius, and density of 2.248+0.117-0.120 Me, 1.167+0.037-0.036 Re, and 7.757+0.889-0.789 g/cm3, respectively. Comparison to super-Earth structure models reveals the planet is likely an iron dominated world. The GJ357 system adds to the small sample of low-mass planetary systems with well constrained masses, and further observational and dynamical follow-up is warranted to better understand the overall population of small multi-planet systems in the solar neighbourhood.
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