Much has been written about the benefits of green infrastructure, but securing the resources necessary for its development and long-term maintenance is often difficult. This article’s premise is that, in general, people and organisations will take action to provide those resources when they can see value accruing to them; therefore narratives of value generation and capture (our definition of business models) are required to motivate and support that action. This article explores the application of soft systems methodology to the wicked problem of business model development in the context of a social enterprise, using a case study based on a piece of green infrastructure in the city of Birmingham, UK, called The Lost World. The research involved a workshop with several of The Lost World’s key stakeholders and aimed at identifying: The Lost World’s scope as a business; its potential value streams; and how they might be realised in a social enterprise. Analysis of the findings shows that while stakeholders can identify opportunities for their organisations, bringing those opportunities to fruition is difficult. The research demonstrates a compelling need for social entrepreneurs to act as catalysts and long-term enablers of the formulation and maintenance of businesses and business models—vital missing actors in the ambition to transform cityscapes.