Contact Center - No Hold Music when truly "on hold"

When truly "on hold" with a contact center agent, there is not an opportunity for hold music or messaging to play. The system offers that functionality all through the IVR, call queues, interrupt messages, etc., but once an agent engages a caller, the ability to hear music or messaging while "on hold" disappears. The same is true for each part of our IVR within the contact center.