I've been thinking about this for a while, and I just had to give it a try.
Arcanine @ Leftovers/Life Orb
Relaxed
188 HP/252 Def/70 Atk
Ability:
Intimidate
Moveset:
-Overheat
-Extremespeed
-HP Ice
-Thunder Fang
Note: This is done assuming the Arcanine has these IVs: 31/30/30/31/31/31.
Ironically, even with a -speed nature, it reaches 203 speed with no speed EVs, enough to outspeed an AgiliGross before an Agility. However, this set focuses more on the defense rather than offense. The EVs are for max lefties recovery, and lemme stop there for a sec. Although you could max the HP for 384 HP (optimal Lefties recovery), you wouldn't have as much EVs leftover for the defense and offense.
It needs max defense, as not even base 80 defense and Intimidate can support its horrible defensive typing. The rest can be dumped into attack.
The moveset is quite standard for Arcanine. Extremespeed gives it a strong priority move, and Overheat gives massive STAB. HP Ice is for Garchomp, and Thunder Fang is for opposing Gyaras.
Here are some calcs:
Adamant 252 Atk Heracross' (@ Choice Scarf) Close Combat does: 47.83% - 56.25%
Adamant 16 Atk Gyarados' (@ Leftovers) Waterfall with
1 DD does: 79.89% - 94.02%
Adamant 252 Atk Metagross' (@ Leftovers) EQ does: 56.25% - 66.30%
Jolly 252 Atk Dugtrio's (@ Choice Band) EQ does: 80.98% - 95.38%
Adamant 252 Atk Garchomp's (@ Choice Scarf) EQ does: 82.07% - 96.74%
Impish 6 Atk Gliscor's (@ Leftovers) EQ does: 47.83% - 56.25%
Impish 6 Atk Donphan's (@ Leftovers) EQ does: 58.15% - 68.48%
You have to admit that's pretty impressive for arguably some of the most common switch-ins. It survives a hit from all providing they don't crit.
BUT BARTENDO, IT'S A 2HKO FROM MOST IF NOT ALL. OH NOEZ!!! Well, that's what you have a strong priority move for in Extremespeed.
Let's take a look at the calcs on the offensive side of the ball.
Arcanine's Overheat does to 6 HP Adamant Heracross: 157.28% - 185.10% (after a -1 sp def from Close Combat)
Arcanine's Thunder Fang to 212 HP/180 Def Adamant Gyarados: 56.77% - 66.93%
Arcanine's Overheat does to 104 HP Adamant Metagross: 101.83% - 119.57%
Arcanine's Extremespeed to 6 HP Jolly Dugtrio does: 54.72% - 64.15%
Arcanine's HP Ice to a 6 HP Adamant Garchomp does: 65.92% - 77.37%
Arcanine's HP Ice to a 6 HP Naughty Garchomp does: 73.18% - 86.03%
Arcanine's HP Ice to a 252 HP Impish Gliscor does:73.45% - 86.44%
Arcanine's Overheat to a 252 HP Impish Gliscor does: 54.52% - 64.12%
Arcanine's Overheat to a 252 HP Impish Donphan does: 59.64% - 70.31%
While that's impressive, it's a bit of a dissappointment. Obviously this Arcanine isn't safe on switch-ins from stuff like the above, but it can come in on the OHKO and likely finish it off. All the calcs were done without the use of a Life Orb, but Life Orb is really suicide on something that you want to take a hit with.
I'm not really sure if this is more of me trying to think of a novelty set or something that could actually work, but hey, it's worth a try.