Well, I'm very fortunate to live in a state (Alaska) that allows a person to hunt multiple animals. If a guy wanted to and could afford, you could shoot 2 grizzlies, 3 black bears, unlimited wolves, wolverines, 5 deer, 5 caribou, 1 elk, 1 goat, 1 dall sheep, 1 elk, and 1 moose. There are more, but you would have to draw some special permits for musk ox and bison.
All these hunts are registration or over the counter permits. It sounds all great or to good to be true, but a person can take advantage of these privileges. However, most of all these hunts are fly out (very expensive) or very difficult to get to. Plus, a person needs to know where to go and how to do it.
I try to plan a couple hunts a year and focus on certain high priority species like goat and sheep.
Alaskans are very fortunate to have a large variety of exotic animals to chase.