In this paper we present GumDrop, Georgetown University’s entry at the DISRPT 2019 Shared Task on automatic discourse unit segmentation and connective detection. Our approach relies on model stacking, creating a heterogeneous ensemble of classifiers, which feed into a metalearner for each final task. The system encompasses three trainable component stacks: one for sentence splitting, one for discourse unit segmentation and one for connective detection. The flexibility of each ensemble allows the system to generalize well to datasets of different sizes and with varying levels of homogeneity.