Irregular systems with long-range interactions and multiple clusters are considered. The presence of clusters leads to excessive computational complexity of conventional fast multipole methods (FMM), used for modeling systems with large number of DOFs. To overcome the difficulty, a modification of the classical FMM is suggested. It tackles the very cause of the complication by accounting for higher intensity of fields, generated by clusters in upward and especially in downward translations. Numerical examples demonstrate that, in accordance with theoretical estimations, in typical cases the modified FMM significantly reduces the time expense without loss of the accuracy.