The anomalous results of recent measurements on various b -> s mu(+)mu(-) processes could be initial evidence of physics beyond the standard model (SM). Assuming this to be the case, we entertain the possibility that the underlying new physics also affects the rare nonleptonic decays of the (B) over bar (0)(s) meson. We consider in particular new physics arising from the interactions of a heavy Z' boson and investigate their influence on the decay modes (B) over bar -> (eta, eta', phi)omega, which receive sizable QCD- and electroweak-penguin contributions. These decays are not yet observed, and their rates are estimated to be relatively small in the SM. Taking into account the pertinent constraints, we find that the Z' effects can greatly increase the rates of (B) over bar -> (eta, phi)omega, by as much as two orders of magnitude, with respect to the SM expectations. We have previously shown that (B) over bar (0)(s)-> (eta, phi)pi(0), with similarly suppressed SM rates, could also undergo substantial Z'-induced enhancement. These rare modes can therefore serve as complementary probes of the potential new physics which may be responsible for the b -> s mu(+)mu(-) anomalies.