  Space-based photometry missions produce exquisite light curves that contain a
wealth of stellar variability on a wide range of timescales. Light curves also
typically contain significant instrumental systematics -- spurious,
non-astrophysical trends that are common, in varying degrees, to many light
curves. Empirical systematics-correction approaches using the information in
the light curves themselves have been very successful, but tend to suppress
astrophysical signals, particularly on longer timescales. Unlike its
predecessors, the PLATO mission will use multiple cameras to monitor the same
stars. We present REPUBLIC, a novel systematics-correction algorithm which
exploits this multi-camera configuration to correct systematics that differ
between cameras, while preserving the component of each star's signal that is
common to all cameras, regardless of timescale. Through simulations with
astrophysical signals (star spots and planetary transits), Kepler-like errors,
and white noise, we demonstrate REPUBLIC's ability to preserve long-term
astrophysical signals usually lost in standard correction techniques. We also
explore REPUBLIC's performance with different number of cameras and systematic
properties. We conclude that REPUBLIC should be considered a potential
complement to existing strategies for systematic correction in multi-camera
surveys, with its utility contingent upon further validation and adaptation to
the specific characteristics of the PLATO mission data
