Confirming the existence of a new higher charmonium <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>?</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>4500</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> by the newly released data of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mi>e</mml:mi></mml:mrow><mml:mrow><mml:mo>+</mml:mo></mml:mrow></mml:msup><mml:msup><mml:…

Recently, the BESIII Collaboration published Born cross section of $e^+e^- \to K^+K^- J/\psi$, in which a new vector enhancement structure $Y(4500)$ was observed for first time. The mass resonance is good agreement with our previous prediction $5S$-$4D$ mixing charmonium candidate $\psi(4500)$, while measured width $2\sigma$ larger than theoretical estimate. In this work, we reanalyzed J/\psi$ by introducing two theoretically predicted states $\psi(4220)$ and $\psi(4500)$ as intermediate resonances, found that deviation problem can be resolved. Meanwhile, inclusion established $\psi(4160)$ $\psi(4415)$ further improve fit quality, four sets widely different solutions to $\Gamma_{e^+e^-} \mathcal{B}(\psi J/\psi)$. order better identify properties $Y(4500)$, calculated hadronic transition final $K^+K^- within charmed meson loop mechanism, where fitted branching ratio $\psi(4500) well explained calculation, supporting around 4.5 GeV higher predicted. Finally, also discussed possible signal another $\psi(4380)$ J/\psi$. These research results should an important step constructing family thoroughly solving charmoniumlike $Y$ problem.