The global rise in homelessness calls for urgent and alternative policy solutions. Non-profits and governmental organizations alert about the many challenges faced by people experiencing homelessness (PEH), which include not only the lack of shelter but also the lack of opportunities for personal development. In this context, the capability approach (CA), which underpins the United Nations Sustainable Development Goals (SDGs), provides a comprehensive framework to assess inequity in terms of real opportunities. This paper explores how the CA can be combined with agent-based modelling and reinforcement learning. The goals are: (1) implementing the CA as a Markov Decision Process (MDP), (2) building on such MDP to develop a rich decision-making model that accounts for more complex motivators of behaviour, such as values and needs, and (3) developing an agent-based simulation framework that allows to assess alternative policies aiming to expand or restore people's capabilities. The framework is developed in a real case study of health inequity and homelessness, working in collaboration with stakeholders, non-profits and domain experts. The ultimate goal of the project is to develop a novel agent-based simulation framework, rooted in the CA, which can be replicated in a diversity of social challenges to assess policies in a non-invasive way.