A new survey of muonium states brings the total of binary non-magnetic oxides studied to 30, with normal muonium—the interstitiallytrapped atomic state—found in 15 of these. The number of shallow-donor states of the type known in ZnO now also totals 15, but thereare hints of several others. Tantalizingly, the shallow-donor and deep-atomic states are found to coexist in several of the candidate highpermittivity dielectrics. Highly anisotropic states, resembling anomalous muonium in semiconductors and including examples ofmuonium trapped at oxygen vacancies, complete a spectrum of hyperfine parameters covering five powers of ten. Effective ionizationtemperatures range from 10K for shallow to over 1000K for deep states, with corresponding activation energies between several meVand several eV. The oxide band gap emerges as a parameter controlling the systematics of the deep-to-shallow transition for muoniumand, by inference, monatomic hydrogen