We investigate 3D density and weak lensing profiles of dark matter haloes predicted by a cosmology-rescaling algorithm for N -body simulations . We extend the rescaling method of Angulo & White ( 2010 ) and Angulo & Hilbert ( 2015 ) to improve its performance on intra-halo scales by using models for the concentration-mass-redshift relation based on excursion set theory . The accuracy of the method is tested with numerical simulations carried out with different cosmological parameters . We find that predictions for median density profiles are more accurate than \sim 5 \% for haloes with masses of 10 ^ { 12.0 } -10 ^ { 14.5 } h ^ { -1 } M _ { \sun } for radii 0.05 < r / r _ { 200 \text { m } } < 0.5 , and for cosmologies with \Omega _ { \text { m } } \in [ 0.15 , 0.40 ] and \sigma _ { 8 } \in [ 0.6 , 1.0 ] . For larger radii , 0.5 < r / r _ { 200 \text { m } } < 5 , the accuracy degrades to \sim 20 \% , due to inaccurate modelling of the cosmological and redshift dependence of the splashback radius . For changes in cosmology allowed by current data , the residuals decrease to \lesssim 2 \% up to scales twice the virial radius . We illustrate the usefulness of the method by estimating the mean halo mass of a mock galaxy group sample . We find that the algorithm ’ s accuracy is sufficient for current data . Improvements in the algorithm , particularly in the modelling of baryons , are likely required for interpreting future ( dark energy task force stage IV ) experiments .