We determine the resonant parameters of the vector states $\phi(1680)$ and $\phi(2170)$ by doing a combined fit to the $e^+e^- \to \eta\phi$ cross sections from threshold to $2.85~{\rm GeV}$ measured by BaBar, Belle, BESIII and CMD-3 experiments. The mass $(1678^{+5}_{-3} \pm 7)~{\rm MeV}/c^2$ and the width $(156 \pm 5 \pm 9)~{\rm MeV}$ are obtained for the $\phi(1680)$, and the mass $(2169 \pm 5 \pm 6)~{\rm MeV}/c^2$ and the width $(96^{+17}_{-14} \pm 9)~{\rm MeV}$ for the $\phi(2170)$. The statistical significance 
of $\phi(2170)$ is $7.2\sigma$. Depending on the interference between the $\phi(1680)$, $\phi(2170)$ and a non-resonant $\eta\phi$ amplitude in the nominal fit, we obtain four solutions and $\Gamma^{e^+e^-}_{\phi(1680)}\cdot \BR[\phi(1680)\to\eta\phi] = (79 \pm 4 \pm 16)$, $(127\pm 5 \pm 12)$, $(65^{+5}_{-4} \pm 13)$ or $(215^{+8}_{-5} \pm 11)~{\rm eV}$, and $\Gamma^{e^+e^-}_{\phiy}\cdot \BR[\phi(2170)\to\eta\phi] = (0.56^{+0.03}_{-0.02} \pm 0.07)$, $(0.36^{+0.05}_{-0.03} \pm 0.07)$, $(38 \pm 1 \pm 5)$ or $(41 \pm 2 \pm 6)~{\rm eV}$, respectively. We also search for the production of $X(1750)\to \eta\phi$ and the significance is only $2.0\sigma$, then we determine the upper limit of $\Gamma^{e^+e^-}_{X(1750)}\cdot \BR[X(1750)\to\eta\phi]$ at 90\% confidence level. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Article funded by SCOAP3 and published under licence by Chinese Physical Society and the Institute of High Energy Physics of the Chinese Academy of Science and the Institute of Modern Physics of the Chinese Academy of Sciences and IOP Publishing Ltd.