This note describes how the (single-spell) identification result of the timing-of-events model by Abbring and Van den Berg (2003b) can be extended to a model that accommodates several competing exit risks. The extended model can be used for example to distinguish between the different effects of a benefit sanction on several competing exit risks out of unemployment such as 'finding work' vs. 'exiting the labor force'. By allowing for a flexible dependence structure between competing exit risks and the duration until entry into treatment, the model can take account of selection into treatment and dependencies between competing exit risks by way of unobservables.