Another vote for going to Accuratereloading.com and scanning around for some information. Most recommendations over there will be that your 7mm Mag will work fine (with proper loads), and that if you want to step up to something else, then step up to something legal for Dangerous Game. This means things like the 9.3x62, the .375 H&H, or larger. A new .338 or .325 won’t give you enough more umph! to make a difference, but that .375 can be comforting if nasty stuff comes around.
I don’t know what your situation is or where you’ll be going, but quite a bit of S.A. hunting is on ranches, and many of those ranches raise or breed DG. As a friend’s father said when he went hunting on a ranch there, “Look, I promise not to shoot your rhinoceros, but I won’t die with a rifle in my hands.” YOU may only be hunting plains game, but that may have little bearing on what you can run into.
Also, you’ll probably find that the one hunt for plains game will stir up a powerful thirst to return, and chase the big stuff. If I were getting another rifle to match up to your 7mm, I’d get the .375.
Draw quickly, shoot carefully.
If you can get closer, get closer. If you can get steadier, get steadier.