We study the process $e^{+}e^{-} rightarrow pi^{+}pi^{-}psi(3686)$ using 5.1 $fb^{-1}$ of data collected at 16 center-of-mass energy ($sqrt{s}$) points from 4.008 to 4.600$sim$GeV by the BESIII detector operating at the BEPCII collider. The measured Born cross sections for $e^{+}e^{-}rightarrow pi^{+}pi^{-}psi(3686)$ are consistent with previous results, but with much improved precision. A fit to the cross section shows contributions from two structures: the first has $M=4209.5pm7.4pm1.4$$sim$MeV/$c^{2}$ and $Gamma=80.1pm24.6pm2.9$$sim$MeV, and the second has $M=4383.8pm4.2pm0.8$$sim$MeV/c$^{2}$ and $Gamma=84.2pm12.5pm2.1$$sim$MeV, where the first errors are statistical and the second systematic. The lower-mass resonance is observed in the process $e^{+}e^{-}rightarrow pi^{+}pi^{-}psi(3686)$ for the first time with a statistical significance of $5.8sigma$. A charged charmonium-like structure is observed in the $pi^{pm}psi(3686)$ invariant mass spectrum for data at $sqrt{s} = 4.416~$GeV. A fit with an $S$-wave Breit-Wigner function yields a mass $M=4032.1pm2.4$~$MeV$^{2}$, where the errors are statistical only. However, there are still unresolved discrepancies between the fit model and data. The width of the intermediate state varies in a wide range for different kinematic regions within the data set. Therefore no simple interpretation of the data has been found, and a future data sample with larger statistics and more theoretical input will be required to better understand this issue.
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