I think one alternative to loading down high-powered rounds is to choose a gun that can easily be converted. I have a friend who has his eye on the Thompson Contender, which he claims can easily change calibers just by switching the barrel. I don't know if this is true or if it even requires a gunsmith. He wants to buy one with both .44 mag & .22 lr barrels.

Another way is to pick a gun that can fire multiple calibers. It may not as drastic as going from bear protection to squirrel hunting, but a lever-action chambered in .357 magnum would be pretty diverse: you could load it up with high velocity magnums for deer, then load it down with powderpuff .38 spl for smaller stuff.

Whatever the way of going about it, I agree with Phat that an automatic like an AR would be too finicky with widely varied rounds. Something bolt-action or single shot would probably work best.