This article proposes ‘biopolitics multiple’ as an approach to the heterogeneity of biopolitical technologies deployed to govern migration today. Building on work that has started to develop analytical vocabularies to diagnose biopolitical technologies that work neither by fostering life nor by making people die in a necropolitical sense, it conceptualises ‘extraction’ and ‘subtraction’ as two such technologies that take ‘hold’ of migrants’ lives today. Extraction, explored in the article through a focus on borderzones in Greece, captures the imbrication of biopolitics and value through the ‘outside’ creation of the economic conditions of data circulation. Subtraction, which is analysed in this article through a focus on Calais, captures the practices of (partial) non-governing by taking material and legal terrain away from migrants and reconfiguring convoluted geographies of (forced) hyper-mobility. This move allows us to understand the governmentality of migration beyond binary oppositions such as ‘making live/letting die’, biopolitics/necropolitics and inclusion/exclusion. Biopolítica múltiple: migración, extracción, sustracción