It depends on a lot of stuff. Heck, I owned just a 30-06 for years, and it worked fine. I even hunted groundhog with it. You have to remember, I'm an Ohio Valley deer hunter. My 'ought-sixes have taken whitetail, coyote, groundhog, boar, and one very unlucky chipmunk. The latter was only confirmed by blood splatter.
The '06 can cover a lot of ground. 55 Accelerator can knock a Coyote at 200 yards. 180 grainers will down a moose.
Dangerous game? If I was going to hunt really dangerous big stuff in NA, I'd go with 35 Whelen on the top end, the chances of me doing this are nil, and the idea of a 2 gun battery would probably be out the window anyway.
Groundhog? Out to 50 yards, I'm cool with 22 LR for the second rifle. Beyond that, I'm using the 30-06 or 25-06
Coyote? If I'm doing more than 150 yards on a dog, I'd not use .223 REM. I've got a 25-06. However, I've also nailed them right fine with 30-06 and 165 grainers while deer hunting out to 250 yards.
Therefore assuming NA-only, and anything less than the biggest bears, I'd go with 30-06 and .22 LR.
YMMV
