  Gravitational-wave observations of compact binary coalescences are allowing
us to see black holes and neutron stars further into the universe and recent
results represent the most sensitive searches for compact objects ever
undertaken. Most searches for gravitational waves from compact binary
coalescence currently rely on detecting coincident triggers from multiple
detectors. In this paper, we describe a new method for extrapolating
significance of single-detector signals beyond the live-time of the analysis.
Using this method, we can recover loud signals which only triggered in a single
detector. We demonstrate this method in a search of O3 data, and recover seven
single-detector events with a false alarm rate less than two per year. These
were the same events as discovered in the GWTC-2.1 and GWTC-3 searches in a
single detector, and all but one event from 3-OGC and 4-OGC. Through a campaign
of injected signals, we estimate that the total time--volume sensitivity
increases by a factor of up to $1.20 \pm 0.02$ at a false alarm rate of one per
two years compared to completely ignoring single-detector events.
