  Methods to increase the light scattered from small particles can help improve
the sensitivity of many sensing techniques. Here, we investigate the role
multiple scattering plays in perturbing the scattered signal when a particle is
added to a random scattering environment. Three enhancement factors,
parametrising the effect of different classes of multiple scattering
trajectories on the field perturbation, are introduced and their mean
amplitudes explored numerically in the context of surface plasmon polariton
scattering. We demonstrate that there exists an optimum scatterer density at
which the sensitivity enhancement is maximised, with factors on the order of
$10^2$ achievable. Dependence of the enhancement factors on scatterer
properties are also studied.
