I suppose that it could be done. Certainly a tiger or lion, which are thin skinned animals and more susceptible to shock than thick-skinned game, but hunting conditions vary and so do the opportunities for a shot. Why NOT use a bigger caliber?
Mike Angelides, PH on my recent hunt in Tanzania, commented that the .404 Jeffery I used on buff and eland was a much faster killer of buffalo than a .375 H&H, which is what most of his clients use. The difference in damage between the two calibers was significant, according to him and his brother. On one buff I shot (twice through the shoulder) the damage was massive, both shoulders shattered, lungs destroyed, one bullet passing through the buff and exiting, the other destroyed the off shoulder and was found in the hollow of the off-side upper leg bone surrounded by bone shards. There was no follow-up required on either of two buff shot. The other buff required on shot through both shoulders and fell dead within about 10 feet. I do not think that a smaller caliber, with a lighter bullet, could inflict this level of damage and quick killing.
I see no advantage in using a smaller caliber, lighter bullet on thick-skinned dangerous game. When shooting you want the animal DEAD as soon as possible.