While platial representations are being developed for sedentary entities, a parallel and useful endeavour would be to consider time in so-called "platio-temporal" representations that would also expand notions of mobility in GIScience, that are solely dependent on Euclidean space and time. Besides enhancing such aspects of place and mobility via spatio-temporal, we also include human aspects of these representations via considerations of the sociological notions of mobility via the mobilities paradigm that can systematically introduce representation of both platial information along with mobilities associated with 'moving places.' We condense these aspects into 'platial mobility,' a novel conceptual framework, as an integration in GIScience and the mobilities paradigm in sociology, that denotes movement of places in our platio-temporal and sociology-based representations. As illustrative cases for further study using platial mobility as a framework, we explore its benefits and methodological aspects toward developing better understanding for disaster management, disaster risk reduction and pandemics. We then discuss some of the illustrative use cases to clarify the concept of platial mobility and its application prospects in the areas of disaster management, disaster risk reduction and pandemics. These use cases, which include flood events and the ongoing COVID-19 pandemic, have led to displaced and restricted communities having to change practices and places, which would be particularly amenable to the conceptual framework developed in our work.