Stimulated by the BESIII observation of X(2100), X(2500), and η(2225), we try to pin down new pseudoscalar meson nonets including these states. The analysis of mass spectra and the study of strong decays indicate that X(2120) and η(2225) associated with π(2070) and the predicted kaon K(2150) may form a new pseudoscalar meson nonet. In addition, more experimental data for X(2100) are necessary to determine its structure of nonets. Then, X(2500), X(2370), π(2360), and the predicted kaon K(2414) can be grouped into another new nonet. These assignments to the discussed pseudoscalar states can be further tested in experiment.