  The most massive black holes in our Universe form binaries at the centre of
merging galaxies. The recent evidence for a gravitational-wave (GW) background
from pulsar timing may constitute the first observation that these supermassive
black hole binaries (SMBHBs) merge. Yet, the most massive SMBHBs are out of
reach of interferometric {GW} detectors and are exceedingly difficult to
resolve individually with pulsar timing. These limitations call for unexplored
strategies to detect individual SMBHBs in the uncharted frequency band
$\lesssim10^{-5}\,\rm Hz$ in order to establish their abundance and decipher
the coevolution with their host galaxies. Here we show that SMBHBs imprint
detectable long-term modulations on GWs from stellar-mass binaries residing in
the same galaxy. We determine that proposed deci-Hz GW interferometers
sensitive to numerous stellar-mass binaries could uncover modulations from
$\sim\mathscr{O}(10^{-1}$ - $10^4)$ SMBHBs with masses $\sim\mathscr{O}(10^7$ -
$10^8)\,\rm M_\odot$ out to redshift $z\sim3.5$. This offers a unique
opportunity to map the population of SMBHBs through cosmic time, which might
remain inaccessible otherwise.
