We propose novel thermodynamic inequalities that apply to stationary asymptotically anti-de Sitter (AdS) black holes. These inequalities incorporate the thermodynamic volume and refine the reverse isoperimetric inequality. To assess the validity of our conjectures, we apply them to a wide range of analytical black hole solutions, observing compelling evidence in their favor. Intriguingly, our findings indicate that these inequalities may also apply for black holes of nonspherical horizon topology, as we show their validity as well for thin asymptotically AdS black rings.