Not really a believer in the overkill idea, only one kind of kill and that would be dead.

But, perhaps then I have had an over damage or two.
One memorable one was a coyote, 338 Win Mag at about 60 steps, 225 grain TSX. This resulted in coyote tenderloin pieces hanging on spruce limbs 4 to 5 feet above ground. Not a fur friendly shot.

When I first went to Africa in 1971, I used swaged down .510" bullets meant for the .500 NE in my wildcat .505, for lack of anything better. John Buhmiller 600 grain used to say that the Barnes 600 grain .505 solid made a good soft nose. I took some Barnes soft nose loads along for possible use against thin skin dangerous game in the brush, but never used them for that purpose. Finally I decided to try one of them out on a wildebeest, just to see how it performed. I shot the animal off hand at about 100 yards, getting a firm hit in the shoulder. It flopped down at the hit (the only example of "knock-down power" I have ever seen), then got back up, took one step and collapsed. We found scattered fragments of the bullet around the shattered shoulder blade, but could never locate the bullet itself. There was no exit wound.

On a lighter note, I once watched my friend, Joe Brown, now a retired federal judge, shoot a ground hog with his 1911 Colt .45 automatic. Despite the legendary stopping power of the .45, the ground hog, after being hit squarely in the chest, ran off to its hole, where it died, with the alfalfa sprout he had been munching on still in his mouth.

I do not consider this an overkill, but I will submit my 405 Winchester with the Hornaday Spirepoint on a broken 10point big bodied buck. I punched him just behind the shoulder blade at 6 feet with the first shot as he charged my grunt call to him with my mouth.

The second shot struck the top of the stomach and the impact burst the liver.

Neither bullet exited. He died in about 15 seconds from first shot to last.

40 foot shot on a grey squirel with a 220 Swift, 60 gr. Hornady Spire Point. Recovered one front leg attached to the back leg by a pc. of skin. The rest vanished.
60 yd. shot on a Klipspringer with 250 gr. TSX out of a 9.3 x 62. It was the smallest rifle on the truck. PH advised "try not to hit any bones", even so left a softball sized pass thru. PH then commented "a good taxidermist should be able to clean that up".

Not sure it qualifies as overkill, but most people would have just used a stick. 3 foot Cottonmouth with a .338 Win Mag 225 grain. It was the closest stick at the time.

Have shot deer with a 375 before and the blood spatter on the exit wound side is to be seen to be believed.

I hit a small warthog at 275 paces with my 375 HH 300 grain swift A-frame. I said it was self defence.

guinea-fowl with 416Rigby. Shoot them above the breasts and there is plenty to eat.

Cottontail with a 444 Marlin. Body in two pieces held together only by a length of intestine.

A gray squirrel with a 300 Weatherby Mag. Dang thing would not stop barking at me.