When helping others, experience becomes important, especially in circumstances that involve interacting with different cultures—such as providing services to refugees. When disability is added to refugee status, multiple types of experience become necessary, with cross-sector collaboration serving as a valuable asset. Thus, in our approach, we do not consider the status of being a migrant and the status of being a person with disabilities separately, as that would be contrary to the lived experience of simultaneously being a refugee and person with disabilities. This paper explores the impact of the Russian invasion of Ukraine on the capacity of the Polish and Romanian organizations providing services to Ukrainian refugees in Warsaw and Bucharest, with a particular focus on disabled refugees. Based on 41 interviews with service providers and grass-roots organizations, we find that this unfortunate event functioned as a natural laboratory for practicing, acquiring, and enhancing skills in multiple domains, leading to increased personal and institutional expertise. We examine the differences between Warsaw and Bucharest, with Warsaw having more experience in dealing with incoming flows of immigrants, while Bucharest is a relative newcomer in this respect. Additionally, we consider the distinction between public providers (public administration) and non-governmental organizations, observing the upscaling of the latter. Implications for policy are discussed within the framework of curtailing civic society under the illiberal wave.