Simulations can aid to bridge the gap between the proof-of-concept stage and the engineering of dielectrophoretic devices. We present a simulation method overcoming the limits of fluid-flow based approaches. In our Monte-Carlo-Poisson simulator, the colloidal system is described at the particle resolution. This characteristic allows for taking into account volume forces and particle-particle interactions usually neglected in the continuum approximation. In turn, large number of particles and large systems can be simulated to meet the device design needs. In an experimentally verifiable case study, we discuss the role of the multi-particle interaction in high and moderate density regimes.