  Stimulated by the BESIII observation of $X(2100)$, $X(2500)$, and
$\eta(2225)$, 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 $\eta(2225)$ associated with $\pi(2070)$ 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, $X(2500)$, $X(2370)$, $\pi(2360)$, 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.
