  Halo models and halo occupation distributions (HODs) are important tools to
model the galaxy and matter distribution. We present and assess a new method
for constraining the parameters of HODs using the gravitational lensing shear
around galaxy pairs, galaxy-galaxy-galaxy-lensing (G3L). In contrast to
galaxy-galaxy-lensing, G3L is sensitive to correlations between the per-halo
numbers of galaxies from different populations. We use G3L to probe these
correlations and test the default hypothesis that they are negligible. We
derive a halo model for G3L and validate it with realistic mock data from the
Millennium Simulation and a semi-analytic galaxy model. Then, we analyse public
data from the Kilo-Degree Survey (KiDS), the VISTA Infrared Kilo-Degree Galaxy
Survey (VIKING) and data from the Galaxy And Mass Assembly Survey (GAMA) to
infer the HODs of galaxies at $z<0.5$ in five different stellar mass bins
between $10^{8.5}h^{-2} M_\odot$ and $10^{11.5}h^{-2} M_\odot$ and two colours
(red and blue), as well as correlations between satellite numbers. The analysis
recovers the true HODs in the simulated data within the $68\%$ credibility
range. The inferred HODs vary significantly with colour and stellar mass. There
is also strong evidence ($>3\sigma$) for correlations, increasing with halo
mass, between the numbers of red and blue satellites and galaxies with stellar
masses below $10^{10} \Msun. Possible causes of these correlations are the
selection of similar galaxies in different samples, the survey flux limit, or
physical mechanisms like a fixed ratio between the satellite numbers of
distinct populations. The decorrelation for halos with smaller masses is
probably an effect of shot noise by low-occupancy halos. The inferred HODs can
be used to complement galaxy-galaxy-lensing or galaxy clustering HOD studies or
as input to cosmological analyses and improved mock galaxy catalogues.
