  This paper builds on two previous works, Lindgren et al. J. Comp. Phys. 371,
712-731 (2018) and Quan et al. arXiv:1807.05384 (2018), to devise a new method
to solve the problem of calculating electrostatic interactions in a system
composed by many dielectric particles, embedded in a homogeneous dielectric
medium, which in turn can also be permeated by charge carriers. The system is
defined by the charge, size, position and dielectric constant of each particle,
as well as the dielectric constant and Debye length of the medium. The effects
of taking into account the dielectric nature of the particles is explored in
selected scenarios where the presence of electrolytes in the medium can
significantly influence the total undergoing interactions. Description of the
mutual interactions between all particles in the system as being truly of
many-body nature reveals how such effects can effectively influence the
magnitudes and even directions of the resulting forces, especially those acting
on particles that have a null net charge. Particular attention is given to a
situation that can be related to colloidal particles in an electrolyte
solution, where it's shown that polarization effects alone can substantially
raise or lower---depending on the dielectric contrast between the particles and
the medium---the energy barrier that divides particle coagulation and
flocculation regions, when an interplay between electrostatic and additional
van der Waals forces is considered. Overall, the results suggest that for an
accurate description of the type of system in question, it is essential to
consider particle polarization if the separation between the interacting
particles are comparable to or smaller than the Debye length of the medium.
