Air transport, acknowledged as the safest and most efficient mode for long-haul travel, is confronted with diverse challenges aimed at improving its environmental performance. A notable aspect of this effort involves the formation of contrails, arising from the emission of water vapor and condensation nuclei in a cold, ice-supersaturated atmosphere, which represents one of the most difficult-to-predict yet physically quantifiable environmental impacts of air traffic. Adopting the bottom-up principle to evaluate individual contrails for trajectory optimization introduces uncertainties in calculating the radiative forcing of contrails and modeling their life cycle. Former studies for modeling the microphysical life cycle of individual contrails based on a 2D Gaussian plume model could be validated with a photographic contrail tracking method in the mid-latitudes. However, contrails rarely form individually over Central Europe; rather, they form as an accumulation behind many aircraft flying through an ice-supersaturated region. For this reason, the 3D Gaussian plume model has been extended for the co-existence of several contrails. The greater the overlap of the contrails, the greater the competition in ice supersaturation between the contrails and therefore the greater the reduction in lifetime compared to single contrails. Furthermore, with increasing overlap, the number density of ice crystals increases, resulting in smaller ice crystals with shorter lifetimes. The overlap effect is also reflected in the angle between non-parallel contrails. The results can be used for further studies on the optical properties of real co-existing contrails.