To implement a circular economy (CE), companies are pushed to innovate, respectively, their business models, from a micro-perspective, and their supply chains, from a meso-perspective. Despite the increasing research on both these perspectives, there is still a knowledge gap on how companies innovate business models and supply chains for circularity. In this study, we build on innovation management, circular business model (CBM), and circular supply chain (CSC) literatures and develop a theory-based framework where circularity leads to product/process/service innovation from a micro-perspective, and to possible innovation in companies’ supply chains (retaining existing chains/renewing them) from a meso-perspective. Through a multiple-case study of Finnish and Italian CE pioneer companies, we validate this framework, find evidence on interplay between CBM and CSC innovation, and identify innovation strategy variants. The framework contributes to innovation management, CBM, and CSC literature works, and encourages managers willing to adopt circularity to consider innovating simultaneously both their business models and supply chains.