In this article we discuss the lived, embodied experience of home-making in relation to identity and belonging through the example of a service-learning project conducted during the COVID-19 pandemic in a higher education setting in London, UK. We also explore the notion of belonging-not-belonging as a cultural, material and embodied construct, inspired by critical pedagogy. We draw on posthumanism, new materialism, intercultural studies, (auto-)ethnography and creative practice research as possible lines of flight in deconstructing the dichotomy between home and a 'foreign' territory-other-than-home that sits at the core of intercultural discourses. We present this project as a possible alternative discourse to (un)do more traditional considerations of home-making as a much more complex construct; in the encounter with new territories, humans and other-than-human artefacts, objects, machines and landscapes, we argue that home-making is a continuous, never-finished process that moves the learner and their teachers continuously. We aim to bring to the forefront new emerging considerations of intercultural studies at the intersection with interdisciplinary, cross-disciplinary and cross-institutional discourses, breaking away from a more traditional and neoliberal view about what belonging means within the context of higher education.