Application Portfolio (AP) complexity is an increasingly important and strongly discussed issue by both researchers and practitioners. Application portfolios in large organizations have become more and more difficult to understand, resulting in costly efforts to maintain and operate them. Although this is an urgent topic in large organizations, researchers and industry experts do not yet have a common understanding of this phenomenon and lack appropriate methods to measure and manage the respective complexity. We conduct an exploratory case study with the central enterprise architecture management (EAM) governance team and ten application owners of a large European automotive company to identify and link root causes and consequences of AP complexity. Furthermore, we evaluate possible solutions to decrease or manage this complexity from an application owners perspective. The results are interpreted from a socio-technical systems perspective.