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Using about $23\text{ }\text{ }\mathrm{f}{\mathrm{b}}^{\ensuremath{-}1}$ of data collected with the BESIII detector operating at the BEPCII storage ring, a precise measurement of the ${e}^{+}{e}^{\ensuremath{-}}\ensuremath{\rightarrow}{\ensuremath{\pi}}^{+}{\ensuremath{\pi}}^{\ensuremath{-}}J/\ensuremath{\psi}$ Born cross section is performed at center-of-mass energies from 3.7730 to 4.7008 GeV. Two structures, identified as the $Y(4220)$ and the $Y(4320)$ states, are observed in …