  Using data samples with a total integrated luminosity of $20.1~\rm fb^{-1}$
collected by the BESIII detector operating at the BEPCII collider, the cross
section of the process $e^+e^- \rightarrow \pi^+\pi^-\psi(3686)$ is measured at
center-of-mass energies between 4.0076 and 4.6984 GeV. The measured cross
section is consistent with previous results, but with much improved precision.
A fit to the measured energy-dependent cross section, which includes three
Breit-Wigner functions and a non-resonant contribution, confirms the existence
of the charmonium-like states $Y(4220)$, $Y(4390)$, and $Y(4660)$. This is the
first observation of the $Y(4660)$ at the BESIII experiment.
