The analytical theory of statistical Coulomb interactions allows to determine the trajectory displacement in a single rotationally symmetrical beam with well-behaved spatial and angular particle distributions. This can be used to estimate the trajectory displacement in a multi-beam system using the so called fully-filled segment approximation. This approach predicts full compensation of trajectory displacement for a specific setup of the system. We show that this prediction is not consistent with Monte Carlo simulations and we develop a new approach to the calculation, showing that two independent trajectory displacement contributions are present in a multi-beam system. We support this calculation with Monte Carlo simulations as well as with experimental data from a multi-beam system.@en