Cyber-attacks pose a security threat to military command and control networks, Intelligence, Surveillance, and Reconnaissance (ISR) systems, and civilian critical national infrastructure. The use of artificial intelligence and autonomous agents in these attacks increases the scale, range, and complexity of this threat and the subsequent disruption they cause. Autonomous Cyber Defence (ACD) agents aim to mitigate this threat by responding at machine speed and at the scale required to address the problem. Sequential decision-making algorithms such as Deep Reinforcement Learning (RL) provide a promising route to create ACD agents. These algorithms focus on a single objective such as minimizing the intrusion of red agents on the network, by using a handcrafted weighted sum of rewards. This approach removes the ability to adapt the model during inference, and fails to address the many competing objectives present when operating and protecting these networks. Conflicting objectives, such as restoring a machine from a back-up image, must be carefully balanced with the cost of associated down-time, or the disruption to network traffic or services that might result. Instead of pursing a Single-Objective RL (SORL) approach, here we present a simple example of a multi-objective network defence game that requires consideration of both defending the network against red-agents and maintaining critical functionality of green-agents. Two Multi-Objective Reinforcement Learning (MORL) algorithms, namely Multi-Objective Proximal Policy Optimization (MOPPO), and Pareto-Conditioned Networks (PCN), are used to create two trained ACD agents whose performance is compared on our Multi-Objective Cyber Defence game. The benefits and limitations of MORL ACD agents in comparison to SORL ACD agents are discussed based on the investigations of this game.