  We present preliminary results of a search for several exclusive charmless
hadronic B decays from electron-positron annihilation data collected by the
BABAR detector near the Y(4S) resonance. These include three-body decay modes
with final states h^{+/-}h^{-/+}h^{+/-} and h^{+/-}h^{-/+}pi^0, and
quasi-two-body decay modes with final states X^0 h and X^0 K0S, where h = pi or
K and X^0 = eta^' or omega. We find B(B^0 --> rho^(-/+)pi^(+/-)) =
(49+/-13^{+6}_{-5}) x 10^{-6} and B(B^+ --> eta^' K^+) = (62+/-18+/-8) x
10^{-6} and present upper limits for eight other decays.
