We present a systematic analysis of the constraints σ_γ on the mass profile slope γ obtainable when fitting a singular power-law ellipsoid model to a typical strong lensing observation of an extended source. These results extend our previous analysis of circular systems, Paper I. We draw our results from 676 mock observations covering a range of image configurations, each created with a fixed signal to noise ratio S = 100 in the images. We analyse the results using a combination of theory and a simplified model which identifies the contribution to the constraints of the individual fluxes and positions in each of the lensed images. The main results are: 1. For any lens ellipticity, the constraints σ_γ for two image systems are well described by the results of Paper I, transformed to elliptical coordinates; 2. We derive an analytical expression for σ_γ for systems with the source aligned with the axis of the lens; 3. For both two-image systems and aligned systems, σ_γ is limited by the flux uncertainties; 4. The constraints for off-axis four-image systems are a factor of two to eight better, depending on source size, than for two-image systems, and improve with increasing lens ellipticity. We show that the constraints on γ in these systems derive from the complementary positional information of the images alone, without using flux. The complementarity improves as the offset of the source from the axis increases, such that the best constraints σ_γ < 0.01, for S = 100, occur when the source approaches the caustic.