  Gravitational wave (GW) detections of binary black holes (BBHs) have shown
evidence for a dearth of component black holes with masses above
$\sim50M_\odot$. This is consistent with expectations of a mass gap due to the
existence of pair-instability supernovae (PISN). We argue that ground-based GW
detectors will be sensitive to BBHs with masses above this gap,
$\gtrsim120\,M_\odot$. With no detections, two years at upgraded sensitivity
(A+) would constrain the local merger rate of these BBHs on the "far side" of
the PISN gap to be lower than $0.01\,\mathrm{yr}^{-1}\mathrm{Gpc}^{-3}$.
Alternatively, with a few tens of events we could constrain the location of the
upper edge of the gap to the percent level. We consider the potential impact of
"interloper" black holes within the PISN mass gap on this measurement. Far side
BBHs would also be observed by future instruments such as Cosmic Explorer (CE),
Einstein Telescope (ET) and LISA, and may dominate the fraction of multi-band
events. We show that by comparing observations from ground and space it is
possible to constrain the merger rate history. Moreover, we find that the upper
edge of the PISN mass gap leaves an imprint on the spectral shape of the
stochastic background of unresolved binaries, which may be accessible with A+
sensitivity. Finally, we show that by exploiting the upper edge of the gap,
these high-mass BBHs can be used as standard sirens to constrain the cosmic
expansion at redshifts of $\sim0.4$, $0.8$, and~$1.5$ with LISA, LIGO-Virgo,
and CE/ET, respectively. These far-side binaries would be the most massive BBHs
LIGO-Virgo could detect.
