The design of future mobility solutions (autonomous vehicles, micromobility solutions, etc.) and the design of the mobility systems they enable are closely coupled. Indeed, knowledge about the intended service of novel mobility solutions would impact their design and deployment process, whilst insights about their technological development could significantly affect transportation management policies. This requires tools to study such a coupling and co-design future mobility systems in terms of different objectives. This paper presents a framework to address such co-design problems. In particular, we leverage the recently developed mathematical theory of co-design to frame and solve the problem of designing and deploying an intermodal mobility system, whereby autonomous vehicles service travel demands jointly with micromobility solutions such as shared bikes and escooters, and public transit, in terms of fleets sizing, vehicle characteristics, and public transit service frequency. Our framework is modular and compositional, allowing one to describe the design problem as the interconnection of its individual components and to tackle it from a system-level perspective. Moreover, it only requires very general monotonicity assumptions and it naturally handles multiple objectives, delivering the rational solutions on the Pareto front and thus enabling policy makers to select a policy. To showcase our methodology, we present a realworld case study for Washington D.C., USA. Our work suggests that it is possible to create user-friendly optimization tools to systematically assess the costs and benefits of interventions, and that such analytical techniques might inform policy-making in the future.