In this paper, we apply the novel Fuzzy First-Order Dominance (F-FOD) methodology to rank migrant subpopulations in Lombardy (Italy), in terms of multidimensional poverty and social fragility, for the year 2014, with the purpose to possibly provide useful support to policy-makers, in targeting relief interventions from poverty and discomfort. The F-FOD methodology allows for the direct comparison of different distributions of poverty and fragility, assessed by means of suitable ordinal multi-indicator systems, so extending to this more complex setting, the usual univariate first-order dominance criterion. It also provides complimentary “incomparability” scores, to assess to what extent the final rankings are reliable or instead forcing. It turns out that the levels of poverty and fragility of migrant subpopulations are quite different and, in particular, that the time since migrations has a key impact, on the identification of most critical cases, which typically involve recently migrated people. Evidence also emerges that the temporal poverty/fragility trajectories of migrants, distinguished by country of origin, follow different paths, suggesting how policy interventions must be properly, and differently, tuned to be effective.