Charge detection mass spectrometry (CDMS) is a single-particle technique where the masses of individual ions are determined by simultaneously measuring their mass-to-charge ratio (m/z) and charge. Ions are usually trapped inside an electrostatic linear ion trap (ELIT) where they oscillate back and forth through a detection cylinder, generating a periodic signal that is analyzed by fast Fourier transforms. The oscillation frequency is related to the ion's m/z, and the magnitude is related to the ion's charge. In early work, multiple ion trapping events were discarded because there was a question about whether ion-ion interactions affected the results. Here, we report trajectory calculations performed to assess the influence of ion-ion interactions when multiple highly charged ions are simultaneously trapped in an ELIT. Ion-ion interactions cause trajectory and energy fluctuations that lead to variations in the oscillation frequencies that in turn degrade the precision and accuracy of the m/z measurements. The peak shapes acquire substantial high and low m/z tails, and the average m/z shifts to a higher value as the number of trapped ions increases. The effects of the ion-ion interactions are proportional to the product of the charges and the square root of the number of trapped ions and depend on the ions' m/z distribution. For the ELIT design examined here, ion-ion interactions limit the m/z resolving power to several hundred for a typical homogeneous ion population.