  Standard detection and analysis techniques for transient gravitational waves
make the assumption that detector data contains, at most, one signal at any
time. As detectors improve in sensitivity, this assumption will no longer be
valid. In this paper we examine how current search techniques for transient
gravitational waves will behave under the presence of more than one signal. We
perform searches on data sets containing time-overlapping compact binary
coalescences. This includes a modelled, matched filter search (PyCBC), and an
unmodelled coherent search, coherent WaveBurst (cWB). Both of these searches
are used by the LIGO-Virgo-KAGRA collaboration. We find that both searches are
capable of identifying both signals correctly when the signals are dissimilar
in merger time, $|\Delta t_c| \geq 1$ second, with PyCBC losing only $1\%$ of
signals for overlapping binary black hole mergers. Both pipelines can find
signal pairings within the region $|\Delta t_c| < 1$ second. However,
clustering routines in the pipelines will cause only one of the two signals to
be recovered, as such the efficiency is reduced. Within this region, we find
that cWB can identify both signals. We also find that matched filter searches
can be modified to provide estimates of the correct parameters for each signal.
