This work investigates how sustainable supply chain management develops within a company and evolves from internal to external practices. Specifically, the relationships among sustainable process management (internal practices), sustainable supply management (external practices), customer pressure and innovativeness are elaborated in a conceptual model, which is tested using a survey approach. Partial least squares (PLS) methodology is applied to data collected from a sample of 77 Italian manufacturing firms. Our results highlight that customer pressure and innovativeness positively and significantly affect SPM. We also observe that SPM fully mediates the relationships between such factors and SSM. Finally, innovativeness negatively and significantly moderates the effect customer pressure has on SPM. This study is relevant because it shows what driving and enabling factors influence the development of SSM, providing guidance for companies that wish to achieve further social and environmental improvements in their supply chains.