If you're running VM pro, you could build a custom menu, record the VM box greeting to include the menu options, and offer more menu options including 9 to offsite transfer... one of the options would have to be timeout to a voice question to actually leave a message in the mailbox. Make as a custom leave action for the user.
Downsides:
1. needs Vm pro
2. needs a customer leave action for everyone who wants this
3. If you're running intuity mode, all the extra greetings in the VM can't be used. This can be confusing
4. You'd need to somehow give access to the user to re-record their custom "menu/greeting" probably a user SC pointed at their own little recording menu.
5. Add items 2 and 5, multiple by the users that want it, and you could be looking at quite a bit of work.
GB