I suspect you're on a Single-level IVR?
If so, and if you can, moving to a Multi-level can make it so that you can have one IVR for the open hours, and one for closed - allowing staff to dial the main company number and press the extension who they want to chat with.
BIG *** - changing from single to multi- will wipe out your IVR, so having everything written down/screen capped is paramount.
We're set with the flag that callers can dial at any time for an extension.
On the after hours IVR our message states that 'it is after hours and limited options are available...' then give them the options, including the answering service.
You could have it have a message about the company and hours, etc. make it about 15-20 seconds long and then send that to the service. (as well as any keypress besides your extensions)
That make sense?
