We search for ψ(3770)→π+π−η, K+K−η, \(p\bar{p}\eta\) , ρ0π+π−η, K+K−π+π−η, \(p\bar{p}\pi^{+}\pi^{-}\eta\) , \(p\bar{p}K^{+}K^{-}\eta\) and \(p\bar{p}K^{+}K^{-}\pi^{0}\) using data samples of 17.3 and 6.5 pb−1 integrated luminosities recorded at the center-of-mass energies of 3.773 and 3.65 GeV, respectively, by the BES-II detector operating at the BEPC collider. We obtain cross section measurements at both energies and upper limits on ψ(3770) decay branching fractions to the final states studied.