Advances in robotic automation, high-performance computing (HPC), and artificial intelligence (AI) encourage us to conceive of science factories: large, general-purpose computation- and AI-enabled self-driving laboratories (SDLs) with the generality and scale needed both to tackle large discovery problems and to support thousands of scientists. Science factories require modular hardware and software that can be replicated for scale and (re)configured to support many applications. To this end, we propose a prototype modular science factory architecture in which reconfigurable modules encapsulating scientific instruments are linked with manipulators to form workcells, that can themselves be combined to form larger assemblages, and linked with distributed computing for simulation, AI model training and inference, and related tasks. Workflows that perform sets of actions on modules can be specified, and various applications, comprising workflows plus associated computational and data manipulation steps, can be run concurrently. We report on our experiences prototyping this architecture and applying it in experiments involving 15 different robotic apparatus, five applications (one in education, two in biology, two in materials), and a variety of workflows, across four laboratories. We describe the reuse of modules, workcells, and workflows in different applications, the migration of applications between workcells, and the use of digital twins, and suggest directions for future work aimed at yet more generality and scalability. Code and data are available at https://ad-sdl.github.io/wei2023 and in the Supplementary Information