  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
instrument's 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.
