The prediction of new high entropy oxides (HEOs) remains a profound challenge due to their inherent chemical complexity. In this work, we combine experimental and computational methods to search for new HEOs in the tetravalent AO₂ family, using exclusively d⁰ and d¹⁰ cations. Our aim is to explain the phase stability of the α-PbO₂ structure, which is found for the medium entropy oxide (Ti, Zr, Hf, Sn)O₂. Using a pairwise approach to approximate the mixing enthalpy, we confirm that α-PbO₂ is the expected lowest energy structure for this material above other candidates including rutile, baddeleyite, and fluorite structures. We also show that no other five-component compound composed of the tetravalent cations considered here is expected to form under solid state synthesis conditions, which we verify experimentally. Ultimately, we conclude that the flexible geometry of the α-PbO₂ structure can be used to understand its stability among tetravalent HEOs.