A program of measuring the light hadrons production in exclusive $e^+e^-\to \rm{hadrons}$ processes is in place at BABAR with the aim to improve the calculation of the hadronic contribution to the muon $g-2$. We present the most recent results obtained by using the full data set of about 470 fb$^{-1}$ collected by the BABAR experiment at the PEP-II $e^+e^-$ collider at a center-of-mass energy of about 10.6~GeV. In particular, we report the results on the channels $e^+e^-\to\pi^+\pi^-\pi^0\pi^0$, $e^+e^-\to\pi^+\pi^-\pi^0\pi^0\pi^0$, $e^+e^-\to\pi^+\pi^-\pi^0\eta$, and $e^+e^-\to\pi^+\pi^-\eta$. The first reaction, in particular, presently gives the main uncertainty on the total hadronic cross section in the energy region between 1 and 2 GeV.