Nowadays team workspaces are widely adopted for multi-user collaboration and digital resource management. To further broaden real-world applications, mainstream team workspaces platforms, such as Google Workspace and Microsoft OneDrive, allow third-party applications (referred to as add-ons) to be integrated into their workspaces, significantly extending the functionality of team workspaces. The powerful multi-user collaboration capabilities and integration of add-ons make team workspaces a central hub for managing shared resources and protecting them against unauthorized access. Due to the collaboration features of team workspaces, add-ons involved in collaborations may bypass the permission isolation enforced by the administrator, unlike in single-user permission management. This paper aims to investigate the permission management landscape of team workspaces add-ons. To this end, we perform an in-depth analysis of the enforced access control mechanism inherent in this ecosystem, considering both multi-user and cross-app features. We identify three potential security risks that can be exploited to cause permission escalation. We then systematically reveal the landscape of permission escalation risks in the current ecosystem. Specifically, we propose an automated tool, TAI, to systematically test all possible interactions within this ecosystem. Our evaluation reveals that permission escalation vulnerabilities are widespread in this ecosystem, with 41 interactions identified as problematic. Our findings should raise an alert to both the team workspaces platforms and third-party developers.