Designing for migrants and asylum seekers requires the involvement of the whole society to improve the integration of citizens coming from countries with different cultures, religions, and life patterns. The design and development of AI companions for a personalized access to services is the horizon chosen to support and improve the inclusion of migrants and refugees both for the effectiveness of the services provided by public administration and local organizations, and for the quality of life of migrants and refugees. AI-based services are at the heart of the Digital Companion for migrants and asylum seekers designed to support more effective communication between public administrations and migrants. The human-centered, iterative, participative and critical design approach proved to be valuable to address the heterogeneous needs of the end-users as well as of the local service providers. Concrete issues in defining, testing, and refining the AI are discussed in view of provoking an impact on the whole society and towards a scenario of full development and upscaling.