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Current searches for the gravitational-wave signature of compact binarymergers rely on matched-filtering data from interferometric observatories withsets of modelled gravitational waveforms. These searches currently use modelwaveforms that do not include the higher-order mode content of thegravitational-wave signal. Higher-order modes are important for many compactbinary mergers and their omission reduces the sensitivity to such sources. Inthis work we explore the sensitivity loss incurred from omitting higher-ordermodes. We present a new method for searching for compact binary mergers usingwaveforms that include higher-order mode effects, and evaluate the sensitivityincrease that using our new method would allow. We find that, when evaluatingsensitivity at a constant rate-of-false alarm, and when including the fact thatsignal-consistency tests can reject some signals that include higher-order modecontent, we observe a sensitivity increase of up to a factor of 2 in volume forhigh mass ratio, high total-mass systems. For systems with equal mass, or withtotal mass $\sim 50 M_{\odot}$, we see more modest sensitivity increases, $<10\%$, which indicates that the existing search is already performing well. Ournew search method is also directly applicable in searches for generic compactbinaries.

Searching for the full symphony of black hole binary mergers