A technique for handling interrupts in a data processing system includes receiving, at an interrupt presentation controller (IPC), an event notification message (ENM) that specifies an event target number and a number of bits to ignore. In response to a slot being available in an interrupt request queue, the IPC enqueues the ENM in the slot. In response to the ENM being dequeued from the interrupt request queue, the IPC determines a group of virtual processor threads that may be potentially interrupted based on the event target number and the number of bits to ignore specified in the ENM. The event target number identifies a specific virtual processor thread and the number of bits to ignore identifies the number of lower-order bits to ignore with respect to the specific virtual processor thread when determining a group of virtual processor threads that may be potentially interrupted.