Ok i can think of a few options here.
you can't do what you want right out of the box.
My question is in this WG is that multiple agents then when on call hits its a single phone number? That you want to be able to update?
Best option would be to call into the IVR then have that set your emergency schedule that routes a number, and if this number changes then route to a dummy user, like On call user and set that user to available forward and then you can log into that user and change the forward number from the tui or gui.
Other better options would be to call in and set the emergency schedule then use custom handlers to set the on call number and update it, etc. You could get more granular and controlled this way.