I don't think Axon can do what you're asking. It can only ring extensions, not outbound numbers...
However, I think I've come up with a plausible work around, although definitely not the best solution:
1) Create an extension for each outbound number you want to ring upon an incoming call
2) Create a ring group with all the extensions added to the list
3) Set-up multiple SIP/VoIP soft phones (which have an auto transfer/forward feature) with the extensions you created in Axon, and then have them set to transfer to the appropriate phone numbers.
Now this is where you'll have to test the set-up because it's based on theoretical hypothesis (so to speak), so there is no telling how it might actually work out in a real world environment.
What I'm concerned about is that Axon may be unable to signal the end of a call (e.g. if the caller hanged up, or if the call was taken on another extension/phone number); but I can't tell from planning whether or not this will occur. I suppose it will depend on the soft-phone being used, if it disconnects a transferred call if the original call stops ringing, it should be fine.. but if it just forwards the call blindly, the phones might keep ringing even if the call has long been answered or disconnected.