Taking the example of conspiracy-related communication online as one form of contentious politics, this study examines the data collection challenges for multidimensional comparative research across platforms, time, and cultural embeddings. It compares the architectures and features relevant to data collection, access regimes, and use cultures for a set of digital platforms and communication venues. Differentiating between actor- and content-based strategies, this study discusses the potentials and limitations of these approaches, considering differences in platforms, temporal dynamics, and cultural embeddings as well as several layers of equivalence. The discussion highlights crucial insights into designing data collection strategies in multidimensional comparative studies.