The Process Hitting is a recently introduced framework designed for the modelling of concurrent systems. Its originality lies in a compact representation of both components of the model and its corresponding actions: each action can modify the status of a component, and is conditioned by the status of at most one other component. This allowed to define very efficient static analysis based on local causality to compute reachability properties. However, in the case of cooperations between components (for example, when two components are supposed to interact with a third one only when they are in a given configuration), the approach leads to an over-approximated interleaving between actions, because of the pure asynchronous semantics of the model. To address this issue, we propose an extended definition of the framework, including priority classes for actions. In this paper, we focus on a restriction of the Process Hitting with two classes of priorities and a specific behaviour of the components, that is sufficient to tackle the aforementioned problem of cooperations. We show that this class of Process Hitting models allows to represent any Asynchronous Discrete Networks, either Boolean or multivalued. Then we develop a new refinement for the under-approximation of the static analysis to give accurate results for this class of Process Hitting models. Our method thus allows to efficiently under-approximate reachability properties in Asynchronous Discrete Networks; it is in particular conclusive on reachability properties in a 94 components Boolean network, which is unprecedented.