A 2D droplet assembly can undergo destabilization through a series of coalescence events that propagate like an avalanche. Multiple avalanches can get triggered during the course of an experiment, which interact as they propagate in the system. In this article, the avalanching phenomenon as a function of the number of avalanches triggered is investigated. The dynamics of interaction between the avalanches is studied as a function of the propensity for propagation of an avalanche and the proximity and asynchrony in triggering. This article shows that when the propagation propensity of avalanches is small, they are uncorrelated and independent allowing one to predict the effect of multiple triggers by a superposition of the results of the single-avalanche case. However, for large propagation propensities, the avalanches compete for droplets to coalesce due to the finite-sized nature of the droplet assembly and behave like a single autocatalytically propagating avalanche. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1111–1118, 2019. © 2018 American Institute of Chemical Engineers