The flow around wheels contributes to a significant part of the aerodynamic drag of passenger vehicles, which is crucial for overall energy efficiency. The rotation and bluff-body geometry of the wheels result in a complex flow field that is sensitive to geometrical variations such as the tyre geometry, tread pattern, tyre deformation and rim design.In this work, wind tunnel tests were performed with a full-scale crossover SUV, using two rim configurations and three tyres. Utilising flow field measurements and time-resolved surface pressure measurements, the main features of the flow were identified for three sets of tyres with distinct shoulder profiles and sidewall geometry. The main differences were found close to the ground. With a narrower sidewall, a smaller contact patch vortex was formed, reducing the drag. Combining the narrow sidewall with a narrow tread, the more rounded shoulder created a larger contact patch vortex and pronounced the vortex from the outer downstream tyre shoulder.Comparing closed and open rims, the same overall flow mechanisms were observed but their relative importance was altered. An interaction between the tyre and rim design was found, mainly in terms of how the front wheel wakes affect the rear wheels.