Drawing on published work from the Asia Pacific Observatory on Health Systems and Policies, this paper presents a framework for undertaking comparative studies on the health systems of countries. Organized under seven types of research approaches, such as national case-studies using a common format, this framework is illustrated using studies of low- and middle-income countries published by the Asia Pacific Observatory. Such studies are important contributions, since much of the health systems research literature comes from high-income countries. No one research approach, however, can adequately analyse a health system, let alone produce a nuanced comparison of different countries. Multiple comparative studies offer a better understanding, as a health system is a complex entity to describe and analyse. Appreciation of context and culture is crucial: what works in one country may not do so in another. Further, a single research method, such as performance indicators, or a study of a particular health system function or component, produces only a partial picture. Applying a comparative framework of several study approaches helps to inform and explain progress against health system targets, to identify differences among countries, and to assess policies and programmes. Multi-method comparative research produces policy-relevant learning that can assist countries to achieve Sustainable Development Goal 3: ensure healthy lives and promoting well-being for all at all ages by 2030.