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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, $|Δt_c| \geq 1$ second, with PyCBC losing only $1\%$ of signals for overlapping binary black hole mergers. Both pipelines can find signal pairings within the region $|Δt_c| < 1$ 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.