Context. The Strong Lensing Legacy Survey (SL2S) provides a sample of the strong lensing events associated with massive distant galaxies, some of which lie in the outskirts of galaxy groups and clusters. Aims. We investigate the internal structure of early-type galaxies in overdense environments, where tidal forces are expected to alter dark matter haloes of infalling galaxies. Methods. SL2SJ02176-0513 is a remarkable lens for the presence of two multiply-imaged systems at different redshifts lensed by a foreground massive galaxy at zlens = 0.656: a bright cusp arc at zarc = 1.847 and an additional double-image system at an estimated redshift of zdbl ~ 2.9 based on photometry and lensing geometry. The system is located about 400 kpc away from the centre of a massive group of galaxies. Mass estimates for the group are available from X-ray observations and satellite kinematics. Multicolour photometry provides an estimate of the stellar mass of the main lens galaxy. The lensing galaxy is modelled with two components (stars and dark matter), and we include the perturbing effect of the group environment and all available constraints. Results. 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 $(\sigma_{\rm grp}=550^{+130}_{-240})$; (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 (α = -1) slope. Conclusions. We demonstrate that multiple source plane systems together with good ancillary dataset can be used to disentangle local and environmental effects.