  Since 2019, GRAVITY has provided direct observations of giant planets and
brown dwarfs at separations of down to 95 mas from the host star. Some of these
observations have provided the first direct confirmation of companions
previously detected by indirect techniques (astrometry and radial velocities).
We want to improve the observing strategy and data reduction in order to lower
the inner working angle of GRAVITY in dual-field on-axis mode. We also want to
determine the current limitations of the instrument when observing faint
companions with separations in the 30-150 mas range. To improve the inner
working angle, we propose a fiber off-pointing strategy during the observations
to maximize the ratio of companion-light-to-star-light coupling in the science
fiber. We also tested a lower-order model for speckles to decouple the
companion light from the star light. We then evaluated the detection limits of
GRAVITY using planet injection and retrieval in representative archival data.
We compare our results to theoretical expectations. We validate our observing
and data-reduction strategy with on-sky observations; first in the context of
brown dwarf follow-up on the auxiliary telescopes with HD 984 B, and second
with the first confirmation of a substellar candidate around the star Gaia DR3
2728129004119806464. With synthetic companion injection, we demonstrate that
the instrument can detect companions down to a contrast of $8\times 10^{-4}$
($\Delta \mathrm{K}= 7.7$ mag) at a separation of 35 mas, and a contrast of
$3\times 10^{-5}$ ($\Delta \mathrm{K}= 11$ mag) at 100 mas from a bright
primary (K<6.5), for 30 min exposure time. With its inner working angle and
astrometric precision, GRAVITY has a unique reach in direct observation
parameter space. This study demonstrates the promising synergies between
GRAVITY and Gaia for the confirmation and characterization of substellar
companions.
