  SL2SJ02176-0513 is a remarkable lens for the presence of two multiply-imaged
systems at different redshifts lensed by a foreground massive galaxy at $z_{\rm
lens}=0.656$: a bright cusp arc at $z_{\rm arc}=1.847$ and an additional
double-image system at an estimated redshift of $z_{\rm dbl}\sim2.9$ based on
photometry and lensing geometry. The system is located about 400 kpc away from
the center of a massive group of galaxies. Mass estimates for the group are
available from X-ray observations and satellite kinematics. Multicolor
photometry provides an estimate of the stellar mass of the main lens galaxy.
The lensing galaxy is modeled with two components (stars and dark matter), and
we include the perturbing effect of the group environment, and all available
constraints. We find that classic lensing degeneracies, e.g. between external
convergence and mass density slope, are significantly reduced with respect to
standard systems and infer tight constraints on the mass density profile: (i)
the dark matter content of the main lens galaxy is in line with that of typical
galaxies $f_{\rm dm}(<R_{\rm e})=0.41^{+0.09}_{-0.06}$; (ii) the required mass
associated with the dark matter halo of the nearby group is consistent with
X-ray and weak-lensing estimates ($\sigma_{\rm grp}=550^{+130}_{-240}$); (iii)
accounting for the group contribution in the form of an external convergence,
the slope of the mass density profile of the main lens galaxy alone is found to
be $\alpha=-1.03^{+0.22}_{-0.16}$, consistent with the isothermal ($\alpha=-1$)
slope. We demonstrate that multiple source plane systems together with good
ancillary dataset can be used to disentangle local and environmental effects.
