Digital twins represent physical systems in virtual space to enable knowledge intensive tasks. For complex physical systems, effective digital integration can often be achieved by means of a system of aggregated digital twins coupled with a services network. Designing such a system of digital twins and services involves a daunting array of options and considerations. This paper presents a design framework that facilitates systematic, effective decisions when designing a system of digital twins to integrate the data from a complex physical system. The design framework is arranged in six steps: 1) needs and constraints analysis, 2) physical system decomposition, 3) services allocation, 4) performance and quality considerations, 5) implementation considerations and 6) veri-fication and validation. The design framework works with a general reference architecture that combines a digital twin aggregation hierarchy with a service-oriented architecture. This reference architecture allows for the separation of concerns, computational load distribution, incremental development and modular software design. The paper considers the merits of the design framework using two illustrative case studies, i.e. a heliostat field and a smart city. The case studies indicate that the design framework can be applied to a wide range of complex systems and can improve the effectiveness of the design process.