Detecting communities in networks is essential for understanding the mesoscopic organization of complex systems. Interactions in most real-world networks evolve over time and exhibit diverse modalities: instantaneous events, continuous contacts that persist over intervals, and delayed interactions where source and destination are temporally separated, as observed in transportation processes. Additionally, interactions may be directed, weighted, or involve multiple node types. Existing methods for community detection in temporal networks typically handle only limited subsets of these features. When applied to real-world data, they often rely on simplifying transformations, such as aggregating interactions into time windows, projecting multipartite structures onto unipartite graphs, or ignoring edge directions and weights, leading to a loss of information. In this work, we generalize Longitudinal Modularity (L-Modularity) and the LAGO algorithm into a unified framework for dynamic community detection in complex link streams. Experiments on three real-world datasets demonstrate that our approach discovers meaningful communities in temporal networks with diverse interaction types.