Health systems’ insurance/funding can be organised in several ways. Some countries have adopted systems with a mixture of public–private involvement (e.g. Australia, Chile, Ireland, South Africa, New Zealand) which creates two-tier health systems, allowing consumers (groups) to have preferential access to the basic standard of care (e.g. skipping waiting times). The degree to which efficiency and equity are achieved in these types of systems is questioned. In this paper, we consider integration of the two tiers by means of a managed competition model, which underpins Social Health Insurance (SHI) systems. We elaborate a two-part conceptual framework, where, first, we review and update the existing pre-requisites for the model of managed competition to fit a broader definition of health systems, and second, we typologise possible roadmaps to achieve that model in terms of the insurance function, and focus on the consequences on providers and governance/stewardship.