a) Notifying a store would be easy, if they can log in and fulfill orders in other stores (or send back a notification).
b) Duplicating the order in another store would be possible via a custom app, though a little messy (delete an order in Store A and create it in Store B).
The challenging part here is how to determine which is the closest store.
If solution A above would work, then you could use Order Automator (automation app my team built) can handle the notification or fulfillment request. Then we’d just need to know the algorithm you’d want to use for determining the closest store. For example: If order shipping state is equal to CA, AZ, NV, OR, WA, notify store A, if it’s in states … notify store B, etc.