I think the OP needs to think a little more about what he really wants or we have misunderstood what he meant in his post.
The .338WM isn't much of a step up from .308 but the .35 Whelen or .358win is? The .338WM will take anything in NA within 400yds. The .35 whelen, not so much. The .358win, certainly not.
Now, if you are just looking for a cool cartridge that is larger diameter than .308, then a BLR in .358win might be just what you are looking for. You would have to reload, but you have the .308 brass.