Against Jacques Derrida’s concept of im-possibility, the paper introduces civil Search and Rescue in the Mediterranean as acts of im-possible solidarity. This solidarity sits with difference, alterity, and incomprehensibility. The analytical lens of solidarity unlocks the inner workings of the current SAR discourse and the civil SAR practices on the high seas. I argue that im-possible solidarity oscillates between fugitive moments, a democracy to come, and the rescuers’ entanglements with the Mediterranean border regime’s coloniality. To unpack how im-possible solidarities remain entangled with the histories and legacies of colonialism and racism, I introduce Akwugo Emejulu’s fugitive feminism to critique the limits of notions of humanity that shape EUrope’s necropolitical border regime and white claims to solidarity.