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