  Based on the updated data of charmoniumlike state $Y(4220)$ reported in the
hidden-charm %and open-charm channels of the $e^+e^-$ annihilation, we propose
a $4S$-$3D$ mixing scheme to categorize $Y(4220)$ into the $J/\psi$ family. We
find that the present experimental data can support this charmonium assignment
to $Y(4220)$. Thus, $Y(4220)$ plays a role of a scaling point in constructing
higher charmonia above 4 GeV. To further test this scenario, we provide more
abundant information on the decay properties of $Y(4220)$, and predict its
charmonium partner $\psi(4380)$, whose evidence is found by analyzing the
$e^+e^-\to \psi(3686)\pi^+\pi^-$ data from BESIII. If $Y(4220)$ is indeed a
charmonium, we must face how to settle the established charmonium $\psi(4415)$
in the $J/\psi$ family. In this work, we may introduce a $5S$-$4D$ mixing
scheme, and obtain the information of the resonance parameters and partial
open-charm decay widths of $\psi(4415)$, which do not contradict the present
experimental data. Additionally, we predict a charmonium partner $\psi(4500)$
of $\psi(4415)$, which can be accessible at future experiments, especially,
BESIII and BelleII. The studies presented in this work provide new insights to
establish the higher charmonium spectrum.
