We present an extension of the BaSTI (Bag of Stellar Tracks and Isochrones) stellar evolution database to extremely metal-poor (Z = 10-5) and super-metal-rich (Z = 0.05) metallicities, with both scaled-solar and α-enhanced ([α/Fe] = 0.4) heavy element distributions. These new tracks (from the pre-main sequence to the early-asymptotic giant branch phase), horizontal branch models, and isochrones will enable the use of the BaSTI database to study the most metal-poor populations found in Local Group faint dwarf galaxies, and the metal-rich component of the Galactic bulge, for example. An overview of several fundamental predictions of stellar evolution over the full metallicity range of BaSTI is presented, together with comparisons with literature calculations at Z = 10-5 and Z = 0.05.