  In this work, we present the mass spectrum of higher charomona around and
above 4.6 GeV by adopting the unquenched potential model. We perform a combined
fit to the updated experimental data of $e^+e^- \to \psi(2S)\pi^+\pi^-$ and
$e^+e^-\to \Lambda_c\bar{\Lambda}_c$. To understand the "platform" structure
observed in the range of $4.57 \sim 4.60$ GeV existing in the
$\Lambda_c\bar{\Lambda}_c$ invariant mass spectrum of $e^+e^-\to
\Lambda_c\bar{\Lambda}_c$ of BESIII, we introduce two resonances in this
combined fit to the $e^+e^- \to \psi(2S)\pi^+\pi^-$ and $e^+e^-\to
\Lambda_c\bar{\Lambda}_c$, which have resonance parameters, $m_{Y_1}=4585\pm2$
MeV, $\Gamma_{Y_1}=29.8\pm8.0$ MeV, $m_{Y_2}=4676\pm7$ MeV, and
$\Gamma_{Y_2}=85.7\pm15.0$ MeV. Furthermore, combining with our theoretical
results, we indicate that the two charmonium-like $Y$ states can be due to two
higher charmonia, which are mixtures of $6S$ and $5D$ $c\bar{c}$ states. Their
two-body open-charm decay behaviors are given. Under the same framework, our
analysis of the data of $e^+e^-\to D_{s}^+D_{s1}(2536)^-$ recently released by
Belle supports to introduce these two higher charmonia around 4.6 GeV.
Additionally, we predict the masses and two-body open-charm decays of six
higher charmonia $\psi(nS)$ and $\psi(mD)$ with $n=7,8,9$ and $m=6,7,8$ above
4.6 GeV. Search for these higher charmonia will be an interesting issue for the
running BESIII and BelleII, and even the possible Super Tau-Charm Factory
discussed in China.
