Under the 'exception management technique' in PRINCE2, the roles most likely to identify issues that exceed stage tolerances are the Project Executive and the Project Manager. The Project Manager monitors the project's progress against its plans and will identify any deviations that might breach the set tolerances. The Project Executive, being accountable for the project's overall success, also plays a crucial role in overseeing tolerance thresholds and taking appropriate actions when these are exceeded.References: (PRINCE2® 7 Foundation Handbook, AXELOS)