The subclass collinear antiferromagnets that break spin Kramers degeneracy—thereby exhibiting ferromagnet-like properties—offer exciting opportunities in magnetism, which motivates the expansion of the material base for these so-called altermagnets. Here, we demonstrate that Ruddlesden–Popper and perovskite phases offer a rich material platform for altermagnetic behavior. Using first-principles calculations, we demonstrate altermagnetism in prototypical nickel-based compounds such as La2NiO4 and identify additional candidates, including the superconducting La3Ni3O7 and the multiferroic BiFeO3. These materials span insulating, semiconducting, and metallic conduction types, with computed nonrelativistic spin splittings reaching up to 250 meV. Our analysis further reveals the presence of accidental nodes and distinct spin-momentum texture topologies at the Brillouin-zone boundary, suggesting a refined classification beyond the initial d-wave and higher even-parity wave classes. Additionally, we address formal inconsistencies in the traditional classification of magnetically ordered systems, proposing resolutions within the altermagnetic framework. Finally, we highlight the potential for altermagnetic behavior of ferrimagnets and weak ferromagnets, broadening the scope for future exploration.