Can Urban Air Mobility (UAM) systems constitute viable and sustainable mobility solutions? This question has increasingly been concerning scientists, companies, policy makers, and authorities as more and more UAM vehicle concepts are seeing the light of day. In order to come closer to answering this question and to demonstrate the dependencies and impacts of the numerous parameters used to describe a highly complex system of a fleet of UAM vehicles operating in an urban environment, this paper employs a System of Systems (SoS) approach. A collaborative SoS framework with an agent-based simulation is introduced, which connects the UAM vehicle design, fleet performance, vertiport network, and reenergizing infrastructure with a Life-Cycle Assessment (LCA). The framework is used to simulate four exemplary UAM fleet-operation scenarios based on two cities and two operational modes, namely urban and suburban operations. Different vehicle design configurations, e.g. multirotor and lift + cruise vehicles, are evaluated in each scenario based on respectively realistic Concepts of Operations (CONOPS). Additionally, two different points in time, namely 2025 and 2050, are considered and assessed for powering the vehicles by taking into account the characteristics of batteries as well as the underlying electricity mix for their operation. Lithium nickel manganese cobalt oxide battery and lithium-sulfur (Li-S) batteries are considered. The SoS framework helps to asses various UAM metrics such as the average wait time for a passenger, the ideal number of aircraft needed for transporting all passengers within given time, the energy required on a vehicle and fleet level, sustainability metrics, e.g. the global warming potential associated with the energy carriers and many more. The capability to explore a wide design space and to visualize the dependencies between the system parameters and their impacts on different SoS metrics provides stakeholders with a helpful tool for their decision making.