The conventional point-to-point setting of Quantum Key Distribution (QKD) typically considers two directly connected remote parties that aim to establish secret keys. However, almost all digital communication tasks involve multiple nodes and complex network architectures. Thus, it is essential to adapt and integrate QKD protocols and their security analyses to accommodate these complex environments and ensure secure communication across interconnected systems. This work proposes a natural generalization of a well-established point-to-point discrete modulated (DM) continuous-variable (CV) QKD protocol to the multi-party setting. We explore four different trust levels among the communicating parties and provide secure key rates in lossy and noisy channels. Our study shows that discrete modulated CV-QKD is a suitable candidate to connect several dozens of users in a point-to-multipoint network, achieving high rates at low cost, using off-the-shelf components employed in modern communication infrastructure.