The prevalent usage of open-source software (OSS) has led to an increased interest in resolving potential third-party security risks by fixing common vulnerabilities and exposures (CVEs). However, even with automated code analysis tools in place, security analysts often lack the means to obtain an overview of vulnerable OSS reuse in large software organizations. In this design study, we propose VulnEx (Vulnerability Explorer), a tool to audit entire software development organizations. We introduce three complementary table-based representations to identify and assess vulnerability exposures due to OSS, which we designed in collaboration with security analysts. The presented tool allows examining problematic projects and applications (repositories), third-party libraries, and vulnerabilities across a software organization. We show the applicability of our tool through a use case and preliminary expert feedback.