As our reliance on critical automated systems grows, the ability to model and analyze their complex behaviors becomes increasingly important. Dov Gabbay’s idea of representing path-dependency on reactive graphs through higher-order arrows – the switches – offers a unified framework for modelling and understanding a wide range of reactive systems. Building on previous work, this paper revisits and extends this approach to a wider context, allowing for many-valued base relations. This means that the base relation, which changes as an effect of crossing arrows, can take values on an arbitrary set instead of simply on and off. We report on the expressivity of many-valued switch graphs in capturing reactivity and how these can concisely represent important classes of reactive systems, including those with fuzzy or probabilistic elements.