In contemplating multilingualism and mobility in the 21st century, several dimensions warrant attention in the emerging field of migration linguistics. First is the move beyond migration to thinking about mobilities, in particular, the new mobilities paradigm in the social sciences which views human mobility as entailing a complex assemblage of movement, social imaginaries, and experience. Second, a study of the different waves of migration in a particular society, as well as concomitant and official language policies -- using Singapore as a case in point -- distinguishes the layers of, on the one hand, the older, and thus established migrants, versus newer migrants, in particular, transient populations of foreign workers, and, crucially, the differential statuses that these communities and their languages hold in society -- including a potential invisibility of authentic multilingualisms. Such an examination allows the development of a typology of migrants in a statal narrative. Where lines are drawn is dependent on circumstance, with the periphery positioned differentially in times of celebration versus crisis, for example, in risk communication in this pandemic era. This holds significant implications for access and appropriation, and consequent (im)mobilities, and, in the bigger picture, for the crucial intersections -- including how society is responding to the role of indigenous languages for the UN's Sustainable Development Goals. This is particularly timely for this International Decade of Indigenous Languages (2022-2032), noted to not be addressing the interactions between language and migration, as well as the challenge of migrant intergration, recognised as a central and important driver of sustainable development.