One deer TAG, one elk TAG ... in Oregon ... HOWEVER ... if you pony up for a Nonresident Hunting license in another state ... Idaho, Montana, Utah, or any other state, paying the Nonresident hunting license snd tag fees, you can purchase Nonresident tags pursuant to their laws. You can only have ONE resident license, issued in the state where you live. If you want to go hunting in Canada, there are other rules; again, the rules of the Canadian province would apply. In many places you would be required to hire a licensed guide.
If you want to hunt a species in Africa, the fact you have a license in Oregon won't mean anything to them ... you'll just have to abide by the laws of that country. IOW: if you have the money, you can go hunting for the rest of your life. Australia, Argentina, Lower Slobovia, the world is wide open ... IF you have the money. But you still get only one elk tag per year in Oregon.
(Note that there are some countries where you might not want to chance it!)