  Using data samples with an integrated luminosity of 19 fb$^{-1}$ at
twenty-eight center-of-mass energies from 3.872 GeV to 4.700 GeV collected with
the BESIII detector at the BEPCII electron--positron collider, the process
$e^{+}e^{-}\to\eta\pi^{+}\pi^{-}$ and the intermediate process
$e^{+}e^{-}\to\eta\rho^{0}$ are studied for the first time. The Born cross
sections are measured. No significant resonance structure is observed in the
cross section lineshape.
