Traditionally, ground vehicle design is based on identifying engineering solutions that fulfil the requirements and specifications put forth by the stakeholders. Although a vehicle is a single entity, it is composed of many subsystems and thousands of parts that must operate together in unison to meet all design goals. A System of Systems (SoS) design approach enables the consideration of subsystem performance within a framework of overall system operation, which includes possible tradeoffs. This collaborative approach to subsystem and primary system design draws upon modelling, optimization, tradespace analysis and virtual studies. In this paper, a system of system design approach will be investigated for a collection of multi-domain vehicles assembled to undertake coordinated search and rescue operations on land and water. A host ground vehicle, an unmanned aerial drone, an unmanned marine drone and an unmanned tracked vehicle constitute the family of multi-domain vehicles which will be used for the search and rescue mission. A digital twin for this family of vehicles will be created to support numerical design studies. The System of Systems approach will enable tradeoffs in vehicle and family design to be evaluated using optimization tools. To visualize the designs, tradespace analysis tools will be key to identifying the tradeoffs and performance at the system level and the individual vehicle level. A case study is undertaken to simulate the trajectory of an aerial drone for a search and rescue operation and calculate its - ilities for such a scenario. In the future, the same exercise will be performed for three other models highlighted above and incorporate their -ilities to incorporate into the subsequent steps of optimization and tradespace analysis. This paper showcases the System of Systems approach and highlights the advantages and challenges faced in implementing such an approach for the purposes of achieving a specific mission through the collaborative and diverse vehicles used.