Precision livestock farming (PLF) is increasingly being suggested as a promising tool for contributing to the sustainable transition of livestock farming as a market system innovation for farm-animal value chains. The innovations of PLF systems are over and above applications aimed at achieving on-farm goals (e.g. improving efficiency and monitoring farm animals), which are well recognised in the existing literature. This paper specifies the new dimensions of PLF systems, including data-sharing with retailers in the chain, with certifiers/control organisations, with other farmers and with market innovators, as well as data governance. Because farmers approach PLF applications that extend beyond on-farm use with reluctance, it is crucial to take farmer preferences into account when designing multi-actor PLF-system innovations. Proceeding from a mixed-method design, this study begins with a literature review and expert interviews, followed by an examination of farmer preferences regarding the architectural-design attributes of a PLF-system innovation. The latter takes the form of a conjoint study based on data obtained from 367 pig and dairy farmers in Finland, the Netherlands and Spain. Results indicate that farmers attach the greatest importance to the governing structure that manages their data, followed by the opportunity to use an on-farm early-warning system to monitor farm animals, and the possibility of sharing the collected data with value-chain actors mainly for purposes of optimising business innovation and certification. A cluster analysis further highlights the importance of finding customised solutions, considering the heterogenous preferences of farmers for PLF-system innovations beyond European borders. These preferences should be considered in the design of multi-actor PLF-system innovations.