Knowledge integration remains, paradoxically, both a key methodology and an elusive mystery in crossdisciplinary work such as interdisciplinary studies, team science, and transdisciplinary research. Many case studies have described compound events and iterations leading to remarkable integrative achievements. Even though a wealth of work on integration indicates that such achievements are common and desirable, there is no context-crossing approach to modeling how multiple integrations can connect to generate larger or more complex integrative results. There is thus an important need to develop an approach for unfolding integration that supports the full variety of integrative practices and theories. In the absence of such an approach, theorists and practitioners must either craft unique accounts for each case--which are difficult both to create and transfer--or reach general conclusions about what the smaller integrations have in common. This article draws upon and contributes to the philosophy of interdisciplinarity, proposing a new, structural approach to modeling connected integrations called integrative topologies. Each topology provides a model of connected integrations that can be customized for different situations instead of starting from scratch or abstracting away from intermediate integrations. First, the article develops simple rules for integrative pathways based on the input-process-output model of integration. Then, the weave, zipper, and chain topologies are introduced along with their hybrids. Next, the article illustrates how integrative topologies can make it easier to teach, plan, facilitate, describe, and evaluate complex combinations of expertise in crossdisciplinary work. The article concludes with areas for future philosophical research on knowledge integration.