Complex and large software-intensive systems are increasingly present in several application domains, including Industry 4.0, connected health, smart cities, and smart agriculture, to mention a few. These systems are commonly composed of diverse other systems often developed by different organizations using various technologies and, as a consequence, interoperability among these systems becomes difficult. Many architectural strategies for interoperability have already been proposed; however, selecting adequate strategies is challenging. Additionally, it lacks an overview of such strategies. This work presents TASIS, a typology of architectural strategies for the interoperability of software-intensive systems. We also validated it with 33 practitioners from different countries with an extensive experience in integration projects. This work also offers 12 industry-based association rules that suggest how to combine those strategies to mitigate issues at different interoperability levels. As a result, our typology can serve as a starting point to further aggregate new strategies and, ultimately, supports software architects in designing interoperability-driven architectural solutions. •It is a typology with architectural strategies and their levels of interoperability.•The typology was created from evidence in literature and validated and refined it.•We offer strategy combinations proven in integration projects, derived from association rules.•Software architects can use it to select architectural strategies for their projects.