Intensive longitudinal data (ILD) have become increasingly common in the social and behavioral sciences; count variables, such as the number of daily smoked cigarettes, are frequently-used outcomes in many ILD studies. We demonstrate a generalized extension of growth mixture modeling (GMM) to Poisson-distributed ILD for identifying qualitatively distinct trajectories in the context of developmental heterogeneity in count data. Accounting for the Poisson outcome distribution is essential for correct model identification and estimation. In addition, setting up the model in a way that is conducive to ILD measures helps with data complexities - large data volume, missing observations, and differences in sampling frequency across individuals. We present technical details of model fitting, summarize an empirical example of patterns of smoking behavior change, and describe research questions the generalized GMM helps to address.