We present a new precision radial velocity (RV) dataset that reveals multiple planets orbiting the stars in the $sim$360 AU, G2$+$G2 twin binary HD 133131AB. Our 6 years of high-resolution echelle observations from MIKE and 5 years from PFS on the Magellan telescopes indicate the presence of two eccentric planets around HD 133131A with minimum masses of 1.43$pm$0.03 and 0.63$pm$0.15 $mathcal{M}_{rm J}$ at 1.44$pm$0.005 and 4.79$pm$0.92 AU, respectively. Additional PFS observations of HD 133131B spanning 5 years indicate the presence of one eccentric planet of minimum mass 2.50$pm$0.05 $mathcal{M}_{rm J}$ at 6.40$pm$0.59 AU, making it one of the longest period planets detected with RV to date. These planets are the first to be reported primarily based on data taken with PFS on Magellan, demonstrating the instruments precision and the advantage of long-baseline RV observations. We perform a differential analysis between the Sun and each star, and between the stars themselves, to derive stellar parameters and measure a suite of 21 abundances across a wide range of condensation temperatures. The host stars are old (likely $sim$9.5 Gyr) and metal-poor ([Fe/H]$sim$-0.30), and we detect a $sim$0.03 dex depletion in refractory elements in HD 133131A versus B (with standard errors $sim$0.017). This detection and analysis adds to a small but growing sample of binary twin exoplanet host stars with precise abundances measured, and represents the most metal-poor and likely oldest in that sample. Overall, the planets around HD 133131A and B fall in an unexpected regime in planet mass-host star metallicity space and will serve as an important benchmark for the study of long period giant planets.
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