Payment Channel Networks (PCNs) provide a means to improve the scaling of cryptocurrency payments by allowing peers to make payments between themselves in an efficient manner. To make a payment between two peers, the task of path planning must first be performed to determine a path in the PCN connecting the peers before the payment is performed using this path. To date, existing research has focused on the problem of performing path planning in PCNs that contain two-party channels. It has been hypothesised that the scaling of PCNs could be further improved by considering the inclusion of multi-party channels that contain more than two peers. However, the problem of performing path planning in PCNs that contain multi-party channels has not yet been considered. In this article, we address this gap in the research literature and propose a novel path planning method for PCNs containing multi-party channels. This method involves modelling the PCN with multi-party channels as a hypergraph, a type of graph where edges can contain two or more vertices, and using this model to solve the path planning problem in question. We prove that the proposed method is correct and computationally efficient. Furthermore, assuming path planning is performed using this method, we also present theoretical and experimental analyses that demonstrate the scaling benefits of using multi-party channels.